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Mathematics Finding the sum of the first $n$ terms of an AP MCQ Questions for Class 10

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Finding the sum of the first $n$ terms of an AP Practice Questions

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Question 1/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(2,5,8,\ldots\) के पहले (10) पदों का योग क्या है?

What is the sum of the first (10) terms of the AP \(2,5,8,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (155)

Explanation

Simple Explanation

यहां (a=2), (d=3), (n=10)। \(S_{10}=\frac{10}{2}[2\cdot2+9\cdot3]=155\)। / Here (a=2), (d=3), (n=10). \(S_{10}=\frac{10}{2}[2\cdot2+9\cdot3]=155\).

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Question 2/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(4,8,12,\ldots\) के पहले (15) पदों का योग ज्ञात कीजिए।

Find the sum of the first (15) terms of the AP \(4,8,12,\ldots\).

Explanation opens after your attempt
Correct Answer

A. (480)

Explanation

Simple Explanation

यहां (a=4) और (d=4) है। \(S_{15}=\frac{15}{2}[8+14\cdot4]=480\)। / Here (a=4) and (d=4). \(S_{15}=\frac{15}{2}[8+14\cdot4]=480\).

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Question 3/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

यदि (a=6), (d=2), (n=20) है तो \(S_n\) क्या होगा?

If (a=6), (d=2), (n=20), what is \(S_n\)?

Explanation opens after your attempt
Correct Answer

B. (500)

Explanation

Simple Explanation

(S_n=\frac{n}{2}[2a+(n-1)d]) लगाएं। \(S_{20}=10[12+38]=500\)। / Use (S_n=\frac{n}{2}[2a+(n-1)d]). \(S_{20}=10[12+38]=500\).

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Question 4/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(1,3,5,\ldots\) के पहले (25) पदों का योग क्या है?

What is the sum of the first (25) terms of the AP \(1,3,5,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (625)

Explanation

Simple Explanation

पहले (n) विषम संख्याओं का योग \(n^2\) होता है। इसलिए \(S_{25}=25^2=625\)। / The sum of the first (n) odd numbers is \(n^2\). So \(S_{25}=25^2=625\).

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Question 5/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(10,20,30,\ldots\) के पहले (12) पदों का योग कितना है?

What is the sum of the first (12) terms of the AP \(10,20,30,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (780)

Explanation

Simple Explanation

यहां (a=10), (d=10), (n=12)। \(S_{12}=6[20+110]=780\)। / Here (a=10), (d=10), (n=12). \(S_{12}=6[20+110]=780\).

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Question 6/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(7,14,21,\ldots\) के पहले (10) पदों का योग क्या होगा?

What will be the sum of the first (10) terms of the AP \(7,14,21,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (385)

Explanation

Simple Explanation

यह (7) के गुणजों की श्रेणी है। (S_{10}=\frac{10}{2}(7+70)=385)। / This is the sequence of multiples of (7). (S_{10}=\frac{10}{2}(7+70)=385).

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Question 7/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

यदि किसी AP का पहला पद (5), अंतिम पद (45) और पदों की संख्या (9) है तो योग क्या है?

If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?

Explanation opens after your attempt
Correct Answer

B. (225)

Explanation

Simple Explanation

जब पहला और अंतिम पद दिए हों तो (S_n=\frac{n}{2}(a+l))। (S_9=\frac{9}{2}(5+45)=225)। / When first and last terms are given use (S_n=\frac{n}{2}(a+l)). (S_9=\frac{9}{2}(5+45)=225).

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Question 8/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(3,6,9,\ldots\) के पहले (30) पदों का योग ज्ञात कीजिए।

Find the sum of the first (30) terms of the AP \(3,6,9,\ldots\).

Explanation opens after your attempt
Correct Answer

A. (1395)

Explanation

Simple Explanation

यहां अंतिम पद (90) है। (S_{30}=\frac{30}{2}(3+90)=1395)। / Here the last term is (90). (S_{30}=\frac{30}{2}(3+90)=1395).

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Question 9/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी \(20,18,16,\ldots\) के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of the AP \(20,18,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (104)

Explanation

Simple Explanation

यह घटती AP है जिसमें (d=-2) है। (S_8=\frac{8}{2}[40+7(-2)]=104)। / This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).

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Question 10/600 Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

यदि AP \(9,13,17,\ldots\) है तो पहले (11) पदों का योग क्या है?

If the AP is \(9,13,17,\ldots\), what is the sum of the first (11) terms?

Explanation opens after your attempt
Correct Answer

A. (319)

Explanation

Simple Explanation

यहां (a=9), (d=4), (n=11)। \(S_{11}=\frac{11}{2}[18+40]=319\)। / Here (a=9), (d=4), (n=11). \(S_{11}=\frac{11}{2}[18+40]=319\).

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