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Mathematics Quiz - Class 10 Mathematics Arithmetic Progre...

Question 1/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(6,9,12,\ldots\) के पहले (14) पदों का योग ज्ञात कीजिए।

Find the sum of the first (14) terms of the arithmetic progression \(6,9,12,\ldots\).

Explanation opens after your attempt

Correct Answer

B. (357)

Step 1

Concept

Here (a=6), (d=3), and (n=14), so \(S_{14}=357\). First identify (a), (d), and (n).

Step 2

Why this answer is correct

The correct answer is B. (357). Here (a=6), (d=3), and (n=14), so \(S_{14}=357\). First identify (a), (d), and (n).

Step 3

Exam Tip

यहाँ (a=6), (d=3), (n=14) है, इसलिए \(S_{14}=357\)। पहले (a), (d), (n) पहचानना सबसे जरूरी है।

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Question 2/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी में पहला पद (4), अंतर (5) और पदों की संख्या (13) है, तो पहले (13) पदों का योग कितना होगा?

If an arithmetic progression has first term (4), common difference (5), and (13) terms, what is the sum of the first (13) terms?

Explanation opens after your attempt

Correct Answer

C. (442)

Step 1

Concept

Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.

Step 2

Why this answer is correct

The correct answer is C. (442). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.

Step 3

Exam Tip

सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) से \(S_{13}=442\) मिलता है। सूत्र में ((n-1)d) ध्यान से लिखें।

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Question 3/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(15,19,23,\ldots\) के पहले (10) पदों का योग क्या है?

What is the sum of the first (10) terms of the arithmetic progression \(15,19,23,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (330)

Step 1

Concept

The tenth term is (51), so (S_{10}=\frac{10}{2}(15+51)=330). Finding the last term first is an easy method.

Step 2

Why this answer is correct

The correct answer is C. (330). The tenth term is (51), so (S_{10}=\frac{10}{2}(15+51)=330). Finding the last term first is an easy method.

Step 3

Exam Tip

दसवाँ पद (51) है, इसलिए (S_{10}=\frac{10}{2}(15+51)=330)। अंतिम पद निकालकर योग लेना आसान तरीका है।

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Question 4/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (22) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (22) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (253)

Step 1

Concept

The sum of the first (n) natural numbers is (\frac{n(n+1)}{2}), so the answer is (253). Put the value of (n) directly in such questions.

Step 2

Why this answer is correct

The correct answer is B. (253). The sum of the first (n) natural numbers is (\frac{n(n+1)}{2}), so the answer is (253). Put the value of (n) directly in such questions.

Step 3

Exam Tip

पहले (n) प्राकृतिक संख्याओं का योग (\frac{n(n+1)}{2}) होता है, इसलिए (253) मिलेगा। ऐसे प्रश्न में सीधे (n) का मान लगाएँ।

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Question 5/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (15) विषम प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (15) odd natural numbers.

Explanation opens after your attempt

Correct Answer

C. (225)

Step 1

Concept

The sum of the first (n) odd numbers is \(n^2\), so \(15^2=225\). This short formula saves time in exams.

Step 2

Why this answer is correct

The correct answer is C. (225). The sum of the first (n) odd numbers is \(n^2\), so \(15^2=225\). This short formula saves time in exams.

Step 3

Exam Tip

पहले (n) विषम संख्याओं का योग \(n^2\) होता है, इसलिए \(15^2=225\)। यह छोटा सूत्र परीक्षा में समय बचाता है।

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Question 6/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (19) सम प्राकृतिक संख्याओं का योग कितना होगा?

What will be the sum of the first (19) even natural numbers?

Explanation opens after your attempt

Correct Answer

B. (380)

Step 1

Concept

The sum of the first (n) even numbers is (n(n+1)), so \(19\times20=380\). Even numbers start from \(2,4,6,\ldots\).

Step 2

Why this answer is correct

The correct answer is B. (380). The sum of the first (n) even numbers is (n(n+1)), so \(19\times20=380\). Even numbers start from \(2,4,6,\ldots\).

Step 3

Exam Tip

पहले (n) सम संख्याओं का योग (n(n+1)) होता है, इसलिए \(19\times20=380\)। सम संख्याएँ \(2,4,6,\ldots\) से शुरू होती हैं।

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Question 7/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी का पहला पद (8), अंतिम पद (62) और कुल पद (10) हैं, तो योग क्या होगा?

If the first term of an arithmetic progression is (8), the last term is (62), and there are (10) terms, what is the sum?

Explanation opens after your attempt

Correct Answer

C. (350)

Step 1

Concept

Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.

Step 2

Why this answer is correct

The correct answer is C. (350). Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.

Step 3

Exam Tip

(S_n=\frac{n}{2}(a+l)) से \(S_{10}=350\)। अंतिम पद दिया हो तो (d) निकालने की जरूरत नहीं होती।

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Question 8/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(40,36,32,\ldots\) के पहले (8) पदों का योग ज्ञात कीजिए।

Find the sum of the first (8) terms of the arithmetic progression \(40,36,32,\ldots\).

Explanation opens after your attempt

Correct Answer

A. (208)

Step 1

Concept

The eighth term is (12), so (S_8=\frac{8}{2}(40+12)=208). In a decreasing progression, take the difference as negative.

Step 2

Why this answer is correct

The correct answer is A. (208). The eighth term is (12), so (S_8=\frac{8}{2}(40+12)=208). In a decreasing progression, take the difference as negative.

Step 3

Exam Tip

आठवाँ पद (12) है, इसलिए (S_8=\frac{8}{2}(40+12)=208)। घटती श्रेणी में अंतर ऋणात्मक लें।

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Question 9/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(7,12,17,\ldots\) के पहले (9) पदों का योग कितना होगा?

What will be the sum of the first (9) terms of the arithmetic progression \(7,12,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (243)

Step 1

Concept

The ninth term is (47), so (S_9=\frac{9}{2}(7+47)=243). With an odd number of terms, the middle term can also check the sum.

Step 2

Why this answer is correct

The correct answer is B. (243). The ninth term is (47), so (S_9=\frac{9}{2}(7+47)=243). With an odd number of terms, the middle term can also check the sum.

Step 3

Exam Tip

नौवाँ पद (47) है, इसलिए (S_9=\frac{9}{2}(7+47)=243)। विषम पदों में मध्य पद से भी योग जाँचा जा सकता है।

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Question 10/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक सभागार में सीटों की पंक्तियाँ \(9,12,15,\ldots\) के क्रम में हैं। पहले (12) पंक्तियों में कुल कितनी सीटें होंगी?

In an auditorium, rows of seats follow \(9,12,15,\ldots\). How many seats will there be in the first (12) rows?

Explanation opens after your attempt

Correct Answer

B. (306)

Step 1

Concept

Here (a=9), (d=3), and (n=12), so there will be (306) seats. In word problems, convert the pattern into an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is B. (306). Here (a=9), (d=3), and (n=12), so there will be (306) seats. In word problems, convert the pattern into an arithmetic progression.

Step 3

Exam Tip

यहाँ (a=9), (d=3), (n=12) है, इसलिए कुल (306) सीटें होंगी। शब्द-प्रश्न में क्रम को समांतर श्रेणी में बदलें।

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Question 11/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि \(S_6=72\) और \(S_{12}=252\) है, तो सातवें से बारहवें पदों का योग कितना है?

If \(S_6=72\) and \(S_{12}=252\), what is the sum of the (7)th to (12)th terms?

Explanation opens after your attempt

Correct Answer

C. (180)

Step 1

Concept

The sum of the (7)th to (12)th terms is \(S_{12}-S_6=180\). Subtract partial sums to find the sum of middle terms.

Step 2

Why this answer is correct

The correct answer is C. (180). The sum of the (7)th to (12)th terms is \(S_{12}-S_6=180\). Subtract partial sums to find the sum of middle terms.

Step 3

Exam Tip

सातवें से बारहवें पदों का योग \(S_{12}-S_6=180\) है। बीच के पदों का योग निकालने के लिए आंशिक योग घटाएँ।

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Question 12/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(3,10,17,\ldots\) के पहले (11) पदों का योग क्या है?

What is the sum of the first (11) terms of the arithmetic progression \(3,10,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (418)

Step 1

Concept

The eleventh term is (73), so (S_{11}=\frac{11}{2}(3+73)=418). Finding the last term correctly is the key step.

Step 2

Why this answer is correct

The correct answer is A. (418). The eleventh term is (73), so (S_{11}=\frac{11}{2}(3+73)=418). Finding the last term correctly is the key step.

Step 3

Exam Tip

ग्यारहवाँ पद (73) है, इसलिए (S_{11}=\frac{11}{2}(3+73)=418)। अंतिम पद सही निकालना मुख्य चरण है।

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Question 13/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

किसी समांतर श्रेणी के पहले (8) पदों का औसत (27) है। इन (8) पदों का योग कितना है?

The average of the first (8) terms of an arithmetic progression is (27). What is the sum of these (8) terms?

Explanation opens after your attempt

Correct Answer

B. (216)

Step 1

Concept

Sum equals average \(\times\) number of terms, so \(27\times8=216\). If the average is given, the long formula is not needed.

Step 2

Why this answer is correct

The correct answer is B. (216). Sum equals average \(\times\) number of terms, so \(27\times8=216\). If the average is given, the long formula is not needed.

Step 3

Exam Tip

योग (=) औसत \(\times\) पदों की संख्या, इसलिए \(27\times8=216\)। औसत मिले तो लंबा सूत्र जरूरी नहीं।

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Question 14/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(18,22,26,\ldots\) के पहले (15) पदों का योग ज्ञात करें।

Find the sum of the first (15) terms of the arithmetic progression \(18,22,26,\ldots\).

Explanation opens after your attempt

Correct Answer

B. (690)

Step 1

Concept

The fifteenth term is (74), so (S_{15}=\frac{15}{2}(18+74)=690). The sum can also be found using the average of the first and last terms.

Step 2

Why this answer is correct

The correct answer is B. (690). The fifteenth term is (74), so (S_{15}=\frac{15}{2}(18+74)=690). The sum can also be found using the average of the first and last terms.

Step 3

Exam Tip

पंद्रहवाँ पद (74) है, इसलिए (S_{15}=\frac{15}{2}(18+74)=690)। पहले और अंतिम पद का औसत लेकर भी योग मिल जाता है।

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Question 15/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक विद्यार्थी प्रतिदिन \(4,8,12,\ldots\) अभ्यास प्रश्न हल करता है। पहले (10) दिनों में कुल कितने प्रश्न हल होंगे?

A student solves \(4,8,12,\ldots\) practice questions per day. How many questions will be solved in the first (10) days?

Explanation opens after your attempt

Correct Answer

C. (220)

Step 1

Concept

This is the sum of the first (10) multiples of (4), so the total is (220) questions. Treat the number of days as (n).

Step 2

Why this answer is correct

The correct answer is C. (220). This is the sum of the first (10) multiples of (4), so the total is (220) questions. Treat the number of days as (n).

Step 3

Exam Tip

यह (4) के पहले (10) गुणजों का योग है, इसलिए कुल (220) प्रश्न होंगे। दिनों की संख्या को (n) मानें।

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Question 16/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी में (a=20), (d=-3), और (n=7) है, तो पहले (7) पदों का योग कितना होगा?

If an arithmetic progression has (a=20), (d=-3), and (n=7), what is the sum of the first (7) terms?

Explanation opens after your attempt

Correct Answer

A. (77)

Step 1

Concept

The seventh term is (2), and (S_7=\frac{7}{2}(20+2)=77). Do not make a sign error with negative (d).

Step 2

Why this answer is correct

The correct answer is A. (77). The seventh term is (2), and (S_7=\frac{7}{2}(20+2)=77). Do not make a sign error with negative (d).

Step 3

Exam Tip

सातवाँ पद (2) है और (S_7=\frac{7}{2}(20+2)=77)। ऋणात्मक (d) में चिन्ह की गलती न करें।

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Question 17/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(25,30,35,\ldots\) के पहले (12) पदों का योग कितना है?

What is the sum of the first (12) terms of the arithmetic progression \(25,30,35,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (630)

Step 1

Concept

The twelfth term is (80), so (S_{12}=\frac{12}{2}(25+80)=630). Keep both the last term and (n) correct.

Step 2

Why this answer is correct

The correct answer is C. (630). The twelfth term is (80), so (S_{12}=\frac{12}{2}(25+80)=630). Keep both the last term and (n) correct.

Step 3

Exam Tip

बारहवाँ पद (80) है, इसलिए (S_{12}=\frac{12}{2}(25+80)=630)। अंतिम पद और (n) दोनों को सही रखें।

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Question 18/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (13) विषम प्राकृतिक संख्याओं का योग क्या होगा?

What will be the sum of the first (13) odd natural numbers?

Explanation opens after your attempt

Correct Answer

B. (169)

Step 1

Concept

The sum of the first (n) odd numbers is \(n^2\), so \(13^2=169\). Remember this pattern for odd numbers.

Step 2

Why this answer is correct

The correct answer is B. (169). The sum of the first (n) odd numbers is \(n^2\), so \(13^2=169\). Remember this pattern for odd numbers.

Step 3

Exam Tip

पहले (n) विषम संख्याओं का योग \(n^2\) है, इसलिए \(13^2=169\)। विषम संख्याओं के लिए यह पैटर्न याद रखें।

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Question 19/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि \(a_n=3n+2\) है, तो पहले (5) पदों का योग ज्ञात कीजिए।

If \(a_n=3n+2\), find the sum of the first (5) terms.

Explanation opens after your attempt

Correct Answer

B. (55)

Step 1

Concept

The first (5) terms are (5,8,11,14,17), whose sum is (55). If \(a_n\) is given, list the terms to check.

Step 2

Why this answer is correct

The correct answer is B. (55). The first (5) terms are (5,8,11,14,17), whose sum is (55). If \(a_n\) is given, list the terms to check.

Step 3

Exam Tip

पहले (5) पद (5,8,11,14,17) हैं, जिनका योग (55) है। \(a_n\) दिया हो तो पद लिखकर जाँचें।

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Question 20/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक बचत योजना में हर महीने जमा राशि \(200,250,300,\ldots\) रुपये है। पहले (8) महीनों की कुल राशि कितनी होगी?

In a savings plan, the monthly deposit is \(200,250,300,\ldots\) rupees. What is the total amount for the first (8) months?

Explanation opens after your attempt

Correct Answer

B. (3000)

Step 1

Concept

Here (a=200), (d=50), and (n=8), so the total is (3000) rupees. In money questions, keep the unit in mind.

Step 2

Why this answer is correct

The correct answer is B. (3000). Here (a=200), (d=50), and (n=8), so the total is (3000) rupees. In money questions, keep the unit in mind.

Step 3

Exam Tip

यहाँ (a=200), (d=50), (n=8) है, इसलिए कुल (3000) रुपये होंगे। राशि वाले प्रश्न में इकाई भी लिखें।

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Question 21/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(2,9,16,\ldots\) के पहले (13) पदों का योग क्या है?

What is the sum of the first (13) terms of the arithmetic progression \(2,9,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (572)

Step 1

Concept

The thirteenth term is (86), so (S_{13}=\frac{13}{2}(2+86)=572). Use ((n-1)d) when finding the last term.

Step 2

Why this answer is correct

The correct answer is D. (572). The thirteenth term is (86), so (S_{13}=\frac{13}{2}(2+86)=572). Use ((n-1)d) when finding the last term.

Step 3

Exam Tip

तेरहवाँ पद (86) है, इसलिए (S_{13}=\frac{13}{2}(2+86)=572)। अंतिम पद निकालते समय ((n-1)d) का उपयोग करें।

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Question 22/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी में \(S_5=65\) और \(S_{11}=242\) है, तो छठे से ग्यारहवें पदों का योग कितना है?

If an arithmetic progression has \(S_5=65\) and \(S_{11}=242\), what is the sum of the (6)th to (11)th terms?

Explanation opens after your attempt

Correct Answer

B. (177)

Step 1

Concept

The sum of the (6)th to (11)th terms is \(S_{11}-S_5=177\). The difference of partial sums gives the answer directly.

Step 2

Why this answer is correct

The correct answer is B. (177). The sum of the (6)th to (11)th terms is \(S_{11}-S_5=177\). The difference of partial sums gives the answer directly.

Step 3

Exam Tip

छठे से ग्यारहवें पदों का योग \(S_{11}-S_5=177\) है। आंशिक योगों का अंतर सीधे उत्तर देता है।

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Question 23/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (17) सम प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (17) even natural numbers.

Explanation opens after your attempt

Correct Answer

B. (306)

Step 1

Concept

The sum of the first (n) even numbers is (n(n+1)), so \(17\times18=306\). Do not confuse (n) with the last even number.

Step 2

Why this answer is correct

The correct answer is B. (306). The sum of the first (n) even numbers is (n(n+1)), so \(17\times18=306\). Do not confuse (n) with the last even number.

Step 3

Exam Tip

पहले (n) सम संख्याओं का योग (n(n+1)) है, इसलिए \(17\times18=306\)। (n) को अंतिम सम संख्या न समझें।

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Question 24/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(60,55,50,\ldots\) के पहले (7) पदों का योग कितना है?

What is the sum of the first (7) terms of the arithmetic progression \(60,55,50,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (315)

Step 1

Concept

The seventh term is (30), so (S_7=\frac{7}{2}(60+30)=315). The same sum formula works for a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. (315). The seventh term is (30), so (S_7=\frac{7}{2}(60+30)=315). The same sum formula works for a decreasing progression.

Step 3

Exam Tip

सातवाँ पद (30) है, इसलिए (S_7=\frac{7}{2}(60+30)=315)। घटती श्रेणी में भी वही योग सूत्र लगता है।

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Question 25/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

किसी समांतर श्रेणी के पहले (6) पदों का योग (126) है। यदि पहले (6) पदों का औसत पूछा जाए, तो वह कितना होगा?

The sum of the first (6) terms of an arithmetic progression is (126). If the average of the first (6) terms is asked, what will it be?

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

Average \(=\frac{126}{6}=21\). The average is found directly from the sum and number of terms.

Step 2

Why this answer is correct

The correct answer is C. (21). Average \(=\frac{126}{6}=21\). The average is found directly from the sum and number of terms.

Step 3

Exam Tip

औसत \(=\frac{126}{6}=21\)। योग और पदों की संख्या से औसत तुरंत मिल जाता है।

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Question 26/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(13,18,23,\ldots\) के पहले (16) पदों का योग ज्ञात कीजिए।

Find the sum of the first (16) terms of the arithmetic progression \(13,18,23,\ldots\).

Explanation opens after your attempt

Correct Answer

A. (808)

Step 1

Concept

The sixteenth term is (88), so (S_{16}=\frac{16}{2}(13+88)=808). For larger (n), find the last term first.

Step 2

Why this answer is correct

The correct answer is A. (808). The sixteenth term is (88), so (S_{16}=\frac{16}{2}(13+88)=808). For larger (n), find the last term first.

Step 3

Exam Tip

सोलहवाँ पद (88) है, इसलिए (S_{16}=\frac{16}{2}(13+88)=808)। बड़े (n) में अंतिम पद पहले निकालें।

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Question 27/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक सीढ़ी में ईंटों की संख्या \(5,10,15,\ldots\) के क्रम में बढ़ती है। पहले (9) स्तरों में कुल कितनी ईंटें लगेंगी?

In a staircase, the number of bricks increases as \(5,10,15,\ldots\). How many bricks will be used in the first (9) levels?

Explanation opens after your attempt

Correct Answer

B. (225)

Step 1

Concept

This is the sum of the first (9) multiples of (5), so \(5\times45=225\). In word problems, treat levels as terms.

Step 2

Why this answer is correct

The correct answer is B. (225). This is the sum of the first (9) multiples of (5), so \(5\times45=225\). In word problems, treat levels as terms.

Step 3

Exam Tip

यह (5) के पहले (9) गुणजों का योग है, इसलिए \(5\times45=225\)। शब्द-प्रश्न में स्तरों को पद मानें।

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Question 28/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि समांतर श्रेणी का पहला पद (11), अंतिम पद (71) और पदों की संख्या (16) है, तो योग कितना होगा?

If the first term of an arithmetic progression is (11), the last term is (71), and the number of terms is (16), what is the sum?

Explanation opens after your attempt

Correct Answer

C. (656)

Step 1

Concept

(S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.

Step 2

Why this answer is correct

The correct answer is C. (656). (S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.

Step 3

Exam Tip

(S_{16}=\frac{16}{2}(11+71)=656)। पहला और अंतिम पद मिले हों तो छोटा सूत्र लगाएँ।

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Question 29/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(8,16,24,\ldots\) के पहले (11) पदों का योग क्या है?

What is the sum of the first (11) terms of the arithmetic progression \(8,16,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (528)

Step 1

Concept

This is the sum of the first (11) multiples of (8), so \(8\times66=528\). For multiples, use the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is B. (528). This is the sum of the first (11) multiples of (8), so \(8\times66=528\). For multiples, use the sum of natural numbers.

Step 3

Exam Tip

यह (8) के पहले (11) गुणजों का योग है, इसलिए \(8\times66=528\)। गुणजों में प्राकृतिक संख्याओं के योग का उपयोग करें।

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Question 30/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (28) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (28) natural numbers.

Explanation opens after your attempt

Correct Answer

C. (406)

Step 1

Concept

\(\frac{28\times29}{2}=406\), so the sum is (406). The natural-number sum formula gives a quick answer.

Step 2

Why this answer is correct

The correct answer is C. (406). \(\frac{28\times29}{2}=406\), so the sum is (406). The natural-number sum formula gives a quick answer.

Step 3

Exam Tip

\(\frac{28\times29}{2}=406\), इसलिए योग (406) है। प्राकृतिक संख्याओं का योग सूत्र जल्दी उत्तर देता है।

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Question 31/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(90,84,78,\ldots\) के पहले (6) पदों का योग कितना होगा?

What will be the sum of the first (6) terms of the arithmetic progression \(90,84,78,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (450)

Step 1

Concept

The sixth term is (60), so (S_6=\frac{6}{2}(90+60)=450). In decreasing order, calculate the last term carefully.

Step 2

Why this answer is correct

The correct answer is B. (450). The sixth term is (60), so (S_6=\frac{6}{2}(90+60)=450). In decreasing order, calculate the last term carefully.

Step 3

Exam Tip

छठा पद (60) है, इसलिए (S_6=\frac{6}{2}(90+60)=450)। घटते क्रम में अंतिम पद की गणना ध्यान से करें।

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Question 32/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी में (a=12), (d=8), और (n=10) है, तो \(S_{10}\) का मान क्या होगा?

If an arithmetic progression has (a=12), (d=8), and (n=10), what will be the value of \(S_{10}\)?

Explanation opens after your attempt

Correct Answer

B. (480)

Step 1

Concept

\(S_{10}=\frac{10}{2}[24+72]=480\). Do the calculation inside the bracket first.

Step 2

Why this answer is correct

The correct answer is B. (480). \(S_{10}=\frac{10}{2}[24+72]=480\). Do the calculation inside the bracket first.

Step 3

Exam Tip

\(S_{10}=\frac{10}{2}[24+72]=480\)। कोष्ठक के अंदर की गणना पहले करें।

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Question 33/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक पौधारोपण अभियान में पौधे \(6,11,16,\ldots\) के क्रम में लगाए जाते हैं। पहले (10) दिनों में कुल कितने पौधे लगाए जाएँगे?

In a plantation campaign, plants are planted in the pattern \(6,11,16,\ldots\). How many plants will be planted in the first (10) days?

Explanation opens after your attempt

Correct Answer

B. (285)

Step 1

Concept

The tenth term is (51), so the total is (S_{10}=\frac{10}{2}(6+51)=285) plants. The same sum formula works in real situations.

Step 2

Why this answer is correct

The correct answer is B. (285). The tenth term is (51), so the total is (S_{10}=\frac{10}{2}(6+51)=285) plants. The same sum formula works in real situations.

Step 3

Exam Tip

दसवाँ पद (51) है, इसलिए कुल (S_{10}=\frac{10}{2}(6+51)=285) पौधे होंगे। वास्तविक स्थितियों में भी योग सूत्र वही रहता है।

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Question 34/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(1,6,11,\ldots\) के पहले (18) पदों का योग कितना है?

What is the sum of the first (18) terms of the arithmetic progression \(1,6,11,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (783)

Step 1

Concept

The eighteenth term is (86), so (S_{18}=\frac{18}{2}(1+86)=783). There are (n-1) common differences.

Step 2

Why this answer is correct

The correct answer is B. (783). The eighteenth term is (86), so (S_{18}=\frac{18}{2}(1+86)=783). There are (n-1) common differences.

Step 3

Exam Tip

अठारहवाँ पद (86) है, इसलिए (S_{18}=\frac{18}{2}(1+86)=783)। (n-1) अंतरों की संख्या होती है।

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Question 35/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि (S_n=\frac{n}{2}(a+l)), (a=14), (l=84), और (n=15) है, तो योग ज्ञात कीजिए।

If (S_n=\frac{n}{2}(a+l)), (a=14), (l=84), and (n=15), find the sum.

Explanation opens after your attempt

Correct Answer

C. (735)

Step 1

Concept

(S_{15}=\frac{15}{2}(14+84)=735). Take the average of the first and last terms and multiply by (n).

Step 2

Why this answer is correct

The correct answer is C. (735). (S_{15}=\frac{15}{2}(14+84)=735). Take the average of the first and last terms and multiply by (n).

Step 3

Exam Tip

(S_{15}=\frac{15}{2}(14+84)=735)। पहले और अंतिम पद का औसत लेकर (n) से गुणा करें।

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Question 36/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (21) सम प्राकृतिक संख्याओं का योग क्या है?

What is the sum of the first (21) even natural numbers?

Explanation opens after your attempt

Correct Answer

B. (462)

Step 1

Concept

The sum of the first (21) even numbers is \(21\times22=462\). Use (n(n+1)) for even numbers.

Step 2

Why this answer is correct

The correct answer is B. (462). The sum of the first (21) even numbers is \(21\times22=462\). Use (n(n+1)) for even numbers.

Step 3

Exam Tip

पहले (21) सम संख्याओं का योग \(21\times22=462\) है। सम संख्याओं के लिए (n(n+1)) प्रयोग करें।

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Question 37/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(17,20,23,\ldots\) के पहले (12) पदों का योग ज्ञात कीजिए।

Find the sum of the first (12) terms of the arithmetic progression \(17,20,23,\ldots\).

Explanation opens after your attempt

Correct Answer

B. (402)

Step 1

Concept

The twelfth term is (50), so (S_{12}=\frac{12}{2}(17+50)=402). Find the last term and apply \(S_n\).

Step 2

Why this answer is correct

The correct answer is B. (402). The twelfth term is (50), so (S_{12}=\frac{12}{2}(17+50)=402). Find the last term and apply \(S_n\).

Step 3

Exam Tip

बारहवाँ पद (50) है, इसलिए (S_{12}=\frac{12}{2}(17+50)=402)। अंतिम पद निकालकर \(S_n\) लगाएँ।

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Question 38/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

किसी समांतर श्रेणी के पहले (9) पदों का योग (198) है। पहले (9) पदों का औसत कितना होगा?

The sum of the first (9) terms of an arithmetic progression is (198). What will be the average of the first (9) terms?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

Average \(=\frac{198}{9}=22\). Dividing the sum by the number of terms gives the average.

Step 2

Why this answer is correct

The correct answer is C. (22). Average \(=\frac{198}{9}=22\). Dividing the sum by the number of terms gives the average.

Step 3

Exam Tip

औसत \(=\frac{198}{9}=22\)। योग को पदों की संख्या से भाग देने पर औसत मिलता है।

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Question 39/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(5,13,21,\ldots\) के पहले (7) पदों का योग कितना होगा?

What will be the sum of the first (7) terms of the arithmetic progression \(5,13,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (203)

Step 1

Concept

The seventh term is (53), so (S_7=\frac{7}{2}(5+53)=203). With an odd number of terms, you can also check using the middle term.

Step 2

Why this answer is correct

The correct answer is A. (203). The seventh term is (53), so (S_7=\frac{7}{2}(5+53)=203). With an odd number of terms, you can also check using the middle term.

Step 3

Exam Tip

सातवाँ पद (53) है, इसलिए (S_7=\frac{7}{2}(5+53)=203)। विषम पदों में मध्य पद से भी जाँच सकते हैं।

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Question 40/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी में \(S_4=44\) और \(S_{9}=189\) है, तो पाँचवें से नौवें पदों का योग कितना है?

If an arithmetic progression has \(S_4=44\) and \(S_9=189\), what is the sum of the (5)th to (9)th terms?

Explanation opens after your attempt

Correct Answer

C. (145)

Step 1

Concept

The sum of the (5)th to (9)th terms is \(S_9-S_4=145\). Subtract the given partial sums to get the answer.

Step 2

Why this answer is correct

The correct answer is C. (145). The sum of the (5)th to (9)th terms is \(S_9-S_4=145\). Subtract the given partial sums to get the answer.

Step 3

Exam Tip

पाँचवें से नौवें पदों का योग \(S_9-S_4=145\) है। दिए गए आंशिक योगों को घटाकर उत्तर लें।

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Question 41/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(16,32,48,\ldots\) के पहले (6) पदों का योग ज्ञात करें।

Find the sum of the first (6) terms of the arithmetic progression \(16,32,48,\ldots\).

Explanation opens after your attempt

Correct Answer

A. (336)

Step 1

Concept

This is the sum of the first (6) multiples of (16), so \(16\times21=336\). For multiples, use \(1+2+\cdots+n\).

Step 2

Why this answer is correct

The correct answer is A. (336). This is the sum of the first (6) multiples of (16), so \(16\times21=336\). For multiples, use \(1+2+\cdots+n\).

Step 3

Exam Tip

यह (16) के पहले (6) गुणजों का योग है, इसलिए \(16\times21=336\)। गुणजों में \(1+2+\cdots+n\) का उपयोग करें।

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Question 42/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि किसी समांतर श्रेणी के पहले (10) पदों का योग (310) है और अंतिम पद (49) है, तो पहला पद कितना होगा?

If the sum of the first (10) terms of an arithmetic progression is (310), and the last term is (49), what is the first term?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

From (310=\frac{10}{2}(a+49)), (a=13). Using the sum formula in reverse also appears in exams.

Step 2

Why this answer is correct

The correct answer is C. (13). From (310=\frac{10}{2}(a+49)), (a=13). Using the sum formula in reverse also appears in exams.

Step 3

Exam Tip

(310=\frac{10}{2}(a+49)) से (a=13)। योग सूत्र को उल्टा लगाना भी परीक्षा में आता है।

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Question 43/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(75,70,65,\ldots\) के पहले (10) पदों का योग कितना है?

What is the sum of the first (10) terms of the arithmetic progression \(75,70,65,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (525)

Step 1

Concept

The tenth term is (30), so (S_{10}=\frac{10}{2}(75+30)=525). The formula for \(S_n\) does not change in decreasing order.

Step 2

Why this answer is correct

The correct answer is B. (525). The tenth term is (30), so (S_{10}=\frac{10}{2}(75+30)=525). The formula for \(S_n\) does not change in decreasing order.

Step 3

Exam Tip

दसवाँ पद (30) है, इसलिए (S_{10}=\frac{10}{2}(75+30)=525)। घटते क्रम में भी \(S_n\) का सूत्र नहीं बदलता।

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Question 44/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

एक दुकान में पैकेट \(7,14,21,\ldots\) की संख्या में रखे गए हैं। पहले (9) शेल्फों में कुल कितने पैकेट होंगे?

In a shop, packets are arranged in the numbers \(7,14,21,\ldots\). How many packets will there be in the first (9) shelves?

Explanation opens after your attempt

Correct Answer

B. (315)

Step 1

Concept

This is the sum of the first (9) multiples of (7), so \(7\times45=315\). Treat the number of shelves as the number of terms.

Step 2

Why this answer is correct

The correct answer is B. (315). This is the sum of the first (9) multiples of (7), so \(7\times45=315\). Treat the number of shelves as the number of terms.

Step 3

Exam Tip

यह (7) के पहले (9) गुणजों का योग है, इसलिए \(7\times45=315\)। शेल्फों की संख्या को पदों की संख्या मानें।

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Question 45/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (16) विषम प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (16) odd natural numbers?

Explanation opens after your attempt

Correct Answer

B. (256)

Step 1

Concept

The sum of the first (n) odd numbers is \(n^2\), so \(16^2=256\). This formula is worth remembering.

Step 2

Why this answer is correct

The correct answer is B. (256). The sum of the first (n) odd numbers is \(n^2\), so \(16^2=256\). This formula is worth remembering.

Step 3

Exam Tip

पहले (n) विषम संख्याओं का योग \(n^2\) होता है, इसलिए \(16^2=256\)। यह सूत्र याद रखने योग्य है।

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Question 46/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

यदि (a=9), (d=9), और (n=8) है, तो समांतर श्रेणी के पहले (8) पदों का योग क्या होगा?

If (a=9), (d=9), and (n=8), what will be the sum of the first (8) terms of the arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (324)

Step 1

Concept

This is the sum of the first (8) multiples of (9), so \(9\times36=324\). If (a=d), the multiples method is faster.

Step 2

Why this answer is correct

The correct answer is C. (324). This is the sum of the first (8) multiples of (9), so \(9\times36=324\). If (a=d), the multiples method is faster.

Step 3

Exam Tip

यह (9) के पहले (8) गुणजों का योग है, इसलिए \(9\times36=324\)। (a=d) हो तो गुणज वाला तरीका तेज है।

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Question 47/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(22,25,28,\ldots\) के पहले (14) पदों का योग ज्ञात कीजिए।

Find the sum of the first (14) terms of the arithmetic progression \(22,25,28,\ldots\).

Explanation opens after your attempt

Correct Answer

B. (581)

Step 1

Concept

The fourteenth term is (61), so (S_{14}=\frac{14}{2}(22+61)=581). Correct calculation of the last term gives the correct sum.

Step 2

Why this answer is correct

The correct answer is B. (581). The fourteenth term is (61), so (S_{14}=\frac{14}{2}(22+61)=581). Correct calculation of the last term gives the correct sum.

Step 3

Exam Tip

चौदहवाँ पद (61) है, इसलिए (S_{14}=\frac{14}{2}(22+61)=581)। अंतिम पद की सही गणना से योग सही मिलता है।

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Question 48/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

किसी समांतर श्रेणी में पहला पद (31), अंतिम पद (13) और पदों की संख्या (7) है। योग कितना होगा?

In an arithmetic progression, the first term is (31), the last term is (13), and the number of terms is (7). What is the sum?

Explanation opens after your attempt

Correct Answer

B. (154)

Step 1

Concept

(S_7=\frac{7}{2}(31+13)=154). The first term can be larger and the last term smaller.

Step 2

Why this answer is correct

The correct answer is B. (154). (S_7=\frac{7}{2}(31+13)=154). The first term can be larger and the last term smaller.

Step 3

Exam Tip

(S_7=\frac{7}{2}(31+13)=154)। पहला पद बड़ा और अंतिम पद छोटा हो सकता है।

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Question 49/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

पहले (35) प्राकृतिक संख्याओं का योग क्या होगा?

What will be the sum of the first (35) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (630)

Step 1

Concept

\(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).

Step 2

Why this answer is correct

The correct answer is C. (630). \(\frac{35\times36}{2}=630\), so the sum is (630). Divide (n(n+1)) by (2).

Step 3

Exam Tip

\(\frac{35\times36}{2}=630\), इसलिए योग (630) है। (n(n+1)) को (2) से भाग दें।

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Question 50/50 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 69

समांतर श्रेणी \(10,18,26,\ldots\) के पहले (12) पदों का योग कितना होगा?

What will be the sum of the first (12) terms of the arithmetic progression \(10,18,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (648)

Step 1

Concept

The twelfth term is (98), so (S_{12}=\frac{12}{2}(10+98)=648). The average of the first and last terms is useful in sums.

Step 2

Why this answer is correct

The correct answer is B. (648). The twelfth term is (98), so (S_{12}=\frac{12}{2}(10+98)=648). The average of the first and last terms is useful in sums.

Step 3

Exam Tip

बारहवाँ पद (98) है, इसलिए (S_{12}=\frac{12}{2}(10+98)=648)। योग में पहले और अंतिम पद का औसत उपयोगी है।

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Class 10 Mathematics - Arithmetic Progressions (AP) - Finding the sum of the first $n$ terms of an AP Easy Quiz

समांतर श्रेणी \(6,9,12,\ldots\) के पहले (14) पदों का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी में पहला पद (4), अंतर (5) और पदों की संख्या (13) है, तो पहले (13) पदों का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(15,19,23,\ldots\) के पहले (10) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

पहले (22) प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

पहले (15) विषम प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

पहले (19) सम प्राकृतिक संख्याओं का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी का पहला पद (8), अंतिम पद (62) और कुल पद (10) हैं, तो योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(40,36,32,\ldots\) के पहले (8) पदों का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(7,12,17,\ldots\) के पहले (9) पदों का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

एक सभागार में सीटों की पंक्तियाँ \(9,12,15,\ldots\) के क्रम में हैं। पहले (12) पंक्तियों में कुल कितनी सीटें होंगी?

Concept

Why this answer is correct

Exam Tip

यदि \(S_6=72\) और \(S_{12}=252\) है, तो सातवें से बारहवें पदों का योग कितना है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(3,10,17,\ldots\) के पहले (11) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

किसी समांतर श्रेणी के पहले (8) पदों का औसत (27) है। इन (8) पदों का योग कितना है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(18,22,26,\ldots\) के पहले (15) पदों का योग ज्ञात करें।

Concept

Why this answer is correct

Exam Tip

एक विद्यार्थी प्रतिदिन \(4,8,12,\ldots\) अभ्यास प्रश्न हल करता है। पहले (10) दिनों में कुल कितने प्रश्न हल होंगे?

Concept

Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी में (a=20), (d=-3), और (n=7) है, तो पहले (7) पदों का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(25,30,35,\ldots\) के पहले (12) पदों का योग कितना है?

Concept

Why this answer is correct

Exam Tip

पहले (13) विषम प्राकृतिक संख्याओं का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n+2\) है, तो पहले (5) पदों का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

एक बचत योजना में हर महीने जमा राशि \(200,250,300,\ldots\) रुपये है। पहले (8) महीनों की कुल राशि कितनी होगी?

Concept

Why this answer is correct