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Class 10 Mathematics - Arithmetic Progressions (AP) - Finding the $n$th term of an AP Hard Quiz

Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Hard Class 10 Level 64

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Question 1/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि किसी समान्तर श्रेणी में \(a_7=31\) और \(a_{19}=103\) है तो \(a_{34}\) का मान क्या होगा?

If in an AP \(a_7=31\) and \(a_{19}=103\), what is the value of \(a_{34}\)?

Explanation opens after your attempt
Correct Answer

B. (193)

Explanation

Simple Explanation

\(d=\frac{103-31}{19-7}=6\) इसलिए \(a_{34}=103+15\times6=193\)। पहले (d) निकालकर निकट पद से आगे बढ़ें। / \(d=\frac{103-31}{19-7}=6\), so \(a_{34}=103+15\times6=193\). First find (d), then move forward from the nearer term.

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Question 2/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_4+a_{16}=86\) और \(a_{10}=43\) है। \(a_{25}\) ज्ञात कीजिए जब सार्व अंतर (5) है।

In an AP, \(a_4+a_{16}=86\) and \(a_{10}=43\). Find \(a_{25}\) when the common difference is (5).

Explanation opens after your attempt
Correct Answer

B. (118)

Explanation

Simple Explanation

\(a_{25}=a_{10}+15d=43+75=118\)। अनावश्यक जानकारी देखकर भ्रमित न हों। / \(a_{25}=a_{10}+15d=43+75=118\). Do not get confused by extra information.

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Question 3/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=3n+p\) और \(a_{12}=50\) है तो \(a_{27}\) क्या होगा?

If \(a_n=3n+p\) and \(a_{12}=50\), what is \(a_{27}\)?

Explanation opens after your attempt
Correct Answer

B. (95)

Explanation

Simple Explanation

(50=36+p) से (p=14) और \(a_{27}=81+14=95\)। पहले स्थिरांक निकालें फिर मांगा पद रखें। / From (50=36+p), (p=14) and \(a_{27}=81+14=95\). First find the constant, then substitute the required term number.

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Question 4/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समान्तर श्रेणी में \(a_{2m}=58\), \(a_{m}=31\) और (d=3) है। (m) का मान क्या है?

In an AP, \(a_{2m}=58\), \(a_m=31\), and (d=3). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

\(a_{2m}-a_m=md=27\) इसलिए (3m=27) और (m=9)। समान्तर श्रेणी में पदों का अंतर स्थान अंतर से जुड़ा होता है। / \(a_{2m}-a_m=md=27\), so (3m=27) and (m=9). In an AP, term difference is linked to position difference.

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Question 5/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(41,35,29,\ldots\) का पहला पद कौन-सा होगा जो (-50) से छोटा है?

Which is the first term of the AP \(41,35,29,\ldots\) that is less than (-50)?

Explanation opens after your attempt
Correct Answer

B. (-53)

Explanation

Simple Explanation

(a_n=41+(n-1)(-6)=47-6n)। (-50) से छोटा पहला पद (-53) है। / (a_n=41+(n-1)(-6)=47-6n). The first term less than (-50) is (-53).

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Question 6/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी का (5)वां पद (x+7) और (12)वां पद (x+42) है तो (20)वां पद (x) के रूप में क्या होगा?

If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?

Explanation opens after your attempt
Correct Answer

C. (x+82)

Explanation

Simple Explanation

(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)। / From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).

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Question 7/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{11}=4a_3\) और \(a_3=18\) है। \(a_{15}\) क्या होगा?

In an AP, \(a_{11}=4a_3\) and \(a_3=18\). What is \(a_{15}\)?

Explanation opens after your attempt
Correct Answer

C. (99)

Explanation

Simple Explanation

\(a_{11}=72\) और (8d=54) इसलिए \(d=\frac{27}{4}\)। \(a_{15}=72+4d=99\)। / \(a_{11}=72\) and (8d=54), so \(d=\frac{27}{4}\). \(a_{15}=72+4d=99\).

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Question 8/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_8=27\) और \(a_{18}=77\) है। वह कौन-सा पद (152) होगा?

In an AP, \(a_8=27\) and \(a_{18}=77\). Which term will be (152)?

Explanation opens after your attempt
Correct Answer

C. (33)वां(33)rd

Explanation

Simple Explanation

\(d=\frac{77-27}{10}=5\)। (152=27+(n-8)5) से (n=33)। / \(d=\frac{77-27}{10}=5\). From (152=27+(n-8)5), (n=33).

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Question 9/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=kn+5\) और \(a_{15}-a_6=63\) है तो \(a_{20}\) क्या होगा?

If \(a_n=kn+5\) and \(a_{15}-a_6=63\), what is \(a_{20}\)?

Explanation opens after your attempt
Correct Answer

C. (145)

Explanation

Simple Explanation

(9k=63) से (k=7)। इसलिए \(a_{20}=7\times20+5=145\)। / From (9k=63), (k=7). Therefore \(a_{20}=7\times20+5=145\).

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Question 10/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(2,9,16,\ldots\) में (200) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (200) in the AP \(2,9,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (205)

Explanation

Simple Explanation

(a_n=2+7(n-1))। (200) से बड़ा पहला पद (205) है क्योंकि पिछला पद (198) है। / (a_n=2+7(n-1)). The first term greater than (200) is (205) because the previous term is (198).

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Question 11/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?

In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

B. (161)

Explanation

Simple Explanation

(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)। / From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).

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Question 12/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी में \(a_3+a_9=72\) है तो \(a_6\) का मान क्या होगा?

If in an AP \(a_3+a_9=72\), what is the value of \(a_6\)?

Explanation opens after your attempt
Correct Answer

C. (36)

Explanation

Simple Explanation

\(a_3\) और \(a_9\) के बीच का पद \(a_6\) है। इसलिए \(a_6=\frac{72}{2}=36\)। / \(a_6\) is the middle term between \(a_3\) and \(a_9\). So \(a_6=\frac{72}{2}=36\).

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Question 13/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक AP में \(a_2+a_5+a_8=111\) है। \(a_5\) का मान ज्ञात कीजिए।

In an AP, \(a_2+a_5+a_8=111\). Find the value of \(a_5\).

Explanation opens after your attempt
Correct Answer

B. (37)

Explanation

Simple Explanation

\(a_2\), \(a_5\), \(a_8\) समान दूरी पर हैं इसलिए उनका मध्य पद औसत है। \(a_5=\frac{111}{3}=37\)। / \(a_2\), \(a_5\), and \(a_8\) are equally spaced, so the middle term is the average. \(a_5=\frac{111}{3}=37\).

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Question 14/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=12\) और \(a_{n}=3a_{n-1}+2\) नहीं बल्कि AP का (a_n=12+(n-1)d) है तथा \(a_9=68\) है तो \(a_{22}\) क्या होगा?

If \(a_1=12\) and it is not \(a_n=3a_{n-1}+2\) but an AP with (a_n=12+(n-1)d), and \(a_9=68\), what is \(a_{22}\)?

Explanation opens after your attempt
Correct Answer

A. (159)

Explanation

Simple Explanation

(68=12+8d) से (d=7)। इसलिए \(a_{22}=12+21\times7=159\)। / From (68=12+8d), (d=7). Therefore \(a_{22}=12+21\times7=159\).

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Question 15/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(5,\frac{13}{2},8,\ldots\) का (30)वां पद क्या है?

What is the (30)th term of the AP \(5,\frac{13}{2},8,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{97}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{3}{2}\)। \(a_{30}=5+29\cdot\frac{3}{2}=\frac{97}{2}\)। / Here \(d=\frac{3}{2}\). \(a_{30}=5+29\cdot\frac{3}{2}=\frac{97}{2}\).

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Question 16/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{10}=0\) और \(a_{21}=-55\) है। \(a_1\) क्या होगा?

In an AP, \(a_{10}=0\) and \(a_{21}=-55\). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

C. (45)

Explanation

Simple Explanation

(11d=-55) से (d=-5)। \(a_1=a_{10}-9d=0+45=45\)। / From (11d=-55), (d=-5). \(a_1=a_{10}-9d=0+45=45\).

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Question 17/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?

If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?

Explanation opens after your attempt
Correct Answer

B. (83)

Explanation

Simple Explanation

(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)। / From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).

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Question 18/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(97,88,79,\ldots\) में (20) से छोटा पहला पद कौन-सा है?

In the AP \(97,88,79,\ldots\), what is the first term less than (20)?

Explanation opens after your attempt
Correct Answer

A. (16)

Explanation

Simple Explanation

इस AP में (d=-9)। पद (25) के बाद (16) आता है इसलिए (20) से छोटा पहला पद (16) है। / In this AP, (d=-9). After the term (25), the next term is (16), so the first term less than (20) is (16).

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Question 19/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि किसी AP का \(a_{14}=a_5+72\) है तो सार्व अंतर क्या है?

If in an AP \(a_{14}=a_5+72\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

\(a_{14}-a_5=9d=72\) इसलिए (d=8)। स्थानों का अंतर हमेशा सीधे (d) से गुणा होता है। / \(a_{14}-a_5=9d=72\), so (d=8). The difference of positions is directly multiplied by (d).

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Question 20/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?

In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)। / \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).

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Question 21/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि AP में \(a_2=2x+1\), \(a_5=5x-2\) और \(a_8=8x-5\) हैं तो \(a_{11}\) क्या होगा?

If in an AP \(a_2=2x+1\), \(a_5=5x-2\), and \(a_8=8x-5\), what is \(a_{11}\)?

Explanation opens after your attempt
Correct Answer

A. (11x-8)

Explanation

Simple Explanation

दिए गए पद समान दूरी पर हैं इसलिए \(a_8-a_5=3x-3\) समान अंतर समूह है। (a_{11}=a_8+(3x-3)=11x-8)। / The given terms are equally spaced, so \(a_8-a_5=3x-3\) is the equal group difference. (a_{11}=a_8+(3x-3)=11x-8).

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Question 22/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(14,23,32,\ldots\) में (300) और (350) के बीच आने वाला सबसे बड़ा पद क्या है?

In the AP \(14,23,32,\ldots\), what is the greatest term between (300) and (350)?

Explanation opens after your attempt
Correct Answer

C. (347)

Explanation

Simple Explanation

पद (14+9(n-1)) के रूप में हैं। (350) से कम सबसे बड़ा उपयुक्त पद (347) है। / The terms are of the form (14+9(n-1)). The greatest suitable term less than (350) is (347).

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Question 23/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n+2}-a_{n}=18\) है और \(a_9=74\) है तो \(a_{25}\) क्या होगा?

If \(a_{n+2}-a_n=18\) and \(a_9=74\), what is \(a_{25}\)?

Explanation opens after your attempt
Correct Answer

C. (218)

Explanation

Simple Explanation

\(a_{n+2}-a_n=2d=18\) इसलिए (d=9)। \(a_{25}=74+16\times9=218\)। / \(a_{n+2}-a_n=2d=18\), so (d=9). \(a_{25}=74+16\times9=218\).

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Question 24/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक AP में \(a_1+a_4=38\) और \(a_7=44\) है। \(a_{16}\) क्या होगा?

In an AP, \(a_1+a_4=38\) and \(a_7=44\). What is \(a_{16}\)?

Explanation opens after your attempt
Correct Answer

B. (80)

Explanation

Simple Explanation

(2a+3d=38) और (a+6d=44)। हल करने पर (d=4) और \(a_{16}=20+60=80\)। / (2a+3d=38) and (a+6d=44). Solving gives (d=4) and \(a_{16}=20+60=80\).

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Question 25/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_6=2a_3+5\) और \(a_3=13\) है तो \(a_{12}\) क्या होगा?

If \(a_6=2a_3+5\) and \(a_3=13\), what is \(a_{12}\)?

Explanation opens after your attempt
Correct Answer

D. (71)

Explanation

Simple Explanation

\(a_6=31\) और (3d=18) इसलिए (d=6)। \(a_{12}=31+6\times6=67\) नहीं बल्कि \(a_{12}=13+9\times6=67\)। / \(a_6=31\) and (3d=18), so (d=6). \(a_{12}=13+9\times6=67\).

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Question 26/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(-7,\frac{-3}{2},4,\ldots\) का (18)वां पद क्या होगा?

What is the (18)th term of the AP \(-7,\frac{-3}{2},4,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{173}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{11}{2}\)। \(a_{18}=-7+17\cdot\frac{11}{2}=\frac{173}{2}\)। / Here \(d=\frac{11}{2}\). \(a_{18}=-7+17\cdot\frac{11}{2}=\frac{173}{2}\).

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Question 27/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{20}=3a_8\) और \(a_8=28\) है तो \(a_{26}\) क्या होगा?

If \(a_{20}=3a_8\) and \(a_8=28\), what is \(a_{26}\)?

Explanation opens after your attempt
Correct Answer

B. (112)

Explanation

Simple Explanation

\(a_{20}=84\) इसलिए (12d=56) और \(d=\frac{14}{3}\)। \(a_{26}=84+6d=112\)। / \(a_{20}=84\), so (12d=56) and \(d=\frac{14}{3}\). \(a_{26}=84+6d=112\).

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Question 28/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{15}=a_5+50\) और \(a_5=24\) है। \(a_{31}\) क्या है?

In an AP, \(a_{15}=a_5+50\) and \(a_5=24\). What is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

B. (154)

Explanation

Simple Explanation

(10d=50) से (d=5)। \(a_{31}=a_5+26d=24+130=154\)। / From (10d=50), (d=5). \(a_{31}=a_5+26d=24+130=154\).

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Question 29/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=an+b\), \(a_4=21\) और \(a_{14}=71\) है तो \(a_{30}\) क्या होगा?

If \(a_n=an+b\), \(a_4=21\), and \(a_{14}=71\), what is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

C. (151)

Explanation

Simple Explanation

(10a=50) से (a=5)। \(a_{30}=a_{14}+16\times5=151\)। / From (10a=50), (a=5). \(a_{30}=a_{14}+16\times5=151\).

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Question 30/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(64,57,50,\ldots\) में (-20) से बड़ा अंतिम पद कौन-सा है?

In the AP \(64,57,50,\ldots\), which is the last term greater than (-20)?

Explanation opens after your attempt
Correct Answer

A. (-13)

Explanation

Simple Explanation

(d=-7) है। (-20) से बड़ा अंतिम पद (-13) है क्योंकि अगला पद (-20) है। / (d=-7). The last term greater than (-20) is (-13) because the next term is (-20).

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Question 31/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक लिफ्ट परीक्षण में पहले चक्र में (240) किग्रा भार है और हर अगले चक्र में (15) किग्रा घटाया जाता है। कौन-से चक्र में भार (75) किग्रा होगा?

In an elevator test, the first cycle has (240) kg load and (15) kg is reduced in each next cycle. In which cycle will the load be (75) kg?

Explanation opens after your attempt
Correct Answer

C. (12)वां(12)th

Explanation

Simple Explanation

(75=240+(n-1)(-15)) से (165=15(n-1)) इसलिए (n=12)। शब्द-प्रश्न में घटाव को ऋणात्मक (d) लें। / From (75=240+(n-1)(-15)), (165=15(n-1)), so (n=12). In word problems, take decrease as negative (d).

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Question 32/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक छात्र पहले दिन (18) प्रश्न हल करता है और प्रतिदिन (4) प्रश्न अधिक हल करता है। किस दिन वह (102) प्रश्न हल करेगा?

A student solves (18) questions on the first day and (4) more questions each day. On which day will he solve (102) questions?

Explanation opens after your attempt
Correct Answer

C. (22)वां(22)nd

Explanation

Simple Explanation

(102=18+(n-1)4) से (84=4(n-1)) इसलिए (n=22)। दैनिक संख्या पद है कुल प्रश्न नहीं। / From (102=18+(n-1)4), (84=4(n-1)), so (n=22). The daily number is the term, not total questions.

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Question 33/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?

If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (15)

Explanation

Simple Explanation

\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें। / From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.

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Question 34/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?

In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)। / \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).

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Question 35/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{12}=5a_4-8\) और \(a_4=17\) है तो \(a_{20}\) क्या होगा?

If \(a_{12}=5a_4-8\) and \(a_4=17\), what is \(a_{20}\)?

Explanation opens after your attempt
Correct Answer

B. (153)

Explanation

Simple Explanation

\(a_{12}=77\) और (8d=60) इसलिए \(d=\frac{15}{2}\)। \(a_{20}=77+8d=137\) नहीं बल्कि \(a_{20}=17+16d=137\)। / \(a_{12}=77\) and (8d=60), so \(d=\frac{15}{2}\). \(a_{20}=17+16d=137\).

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Question 36/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक AP में \(a_9=46\) और \(a_{27}=154\) है। \(a_{18}\) क्या होगा?

In an AP, \(a_9=46\) and \(a_{27}=154\). What is \(a_{18}\)?

Explanation opens after your attempt
Correct Answer

B. (100)

Explanation

Simple Explanation

\(a_{18}\), \(a_9\) और \(a_{27}\) के बीच समान दूरी पर है। इसलिए \(a_{18}=\frac{46+154}{2}=100\)। / \(a_{18}\) is equally spaced between \(a_9\) and \(a_{27}\). Therefore \(a_{18}=\frac{46+154}{2}=100\).

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Question 37/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी \(b-3,b+2,b+7,\ldots\) का (18)वां पद (94) है तो (b) का मान क्या होगा?

If the (18)th term of the AP \(b-3,b+2,b+7,\ldots\) is (94), what is the value of (b)?

Explanation opens after your attempt
Correct Answer

D. (12)

Explanation

Simple Explanation

यहां (d=5)। \(94=b-3+17\times5=b+82\) इसलिए (b=12)। / Here (d=5). \(94=b-3+17\times5=b+82\), so (b=12).

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Question 38/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?

If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)। / (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).

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Question 39/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी AP में \(a_1=52\) और (d=-4) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?

In an AP, \(a_1=52\) and (d=-4). What is the first (n) for which \(a_n\) is negative?

Explanation opens after your attempt
Correct Answer

C. (15)

Explanation

Simple Explanation

(a_n=52-4(n-1)=56-4n)। \(a_n<0\) से (n>14), इसलिए पहला (n=15)। / (a_n=52-4(n-1)=56-4n). From \(a_n<0\), (n>14), so the first (n=15).

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Question 40/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?

If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(72=55+c) से (c=17)। (512=55r+17) से (r=9)। / From (72=55+c), (c=17). From (512=55r+17), (r=9).

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Question 41/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(1000) से कम (17) के धनात्मक गुणजों की AP में अंतिम पद क्या है?

What is the last term in the AP of positive multiples of (17) less than (1000)?

Explanation opens after your attempt
Correct Answer

B. (986)

Explanation

Simple Explanation

(17n<1000) में सबसे बड़ा (n=58) है। अंतिम पद \(17\times58=986\) होगा। / In (17n<1000), the greatest (n=58). The last term will be \(17\times58=986\).

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Question 42/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(250) से बड़े (13) के गुणजों की AP \(260,273,286,\ldots\) है। इसका (22)वां पद क्या होगा?

The AP of multiples of (13) greater than (250) is \(260,273,286,\ldots\). What is its (22)nd term?

Explanation opens after your attempt
Correct Answer

B. (533)

Explanation

Simple Explanation

यहां (a=260) और (d=13)। \(a_{22}=260+21\times13=533\)। / Here (a=260) and (d=13). \(a_{22}=260+21\times13=533\).

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Question 43/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_4+a_{12}=64\) और \(a_8+a_{16}=112\) है। \(a_{20}\) क्या होगा?

In an AP, \(a_4+a_{12}=64\) and \(a_8+a_{16}=112\). What is \(a_{20}\)?

Explanation opens after your attempt
Correct Answer

B. (84)

Explanation

Simple Explanation

पहले योग से (2a+14d=64) और दूसरे से (2a+22d=112)। (8d=48) से (d=6) और \(a_{20}=84\)। / The first sum gives (2a+14d=64) and the second gives (2a+22d=112). From (8d=48), (d=6) and \(a_{20}=84\).

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Question 44/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_3=10\) और \(a_7=2a_3+12\) है तो \(a_{19}\) क्या होगा?

If \(a_3=10\) and \(a_7=2a_3+12\), what is \(a_{19}\)?

Explanation opens after your attempt
Correct Answer

D. (104)

Explanation

Simple Explanation

\(a_7=32\) और (4d=22) इसलिए \(d=\frac{11}{2}\)। \(a_{19}=10+16\cdot\frac{11}{2}=98\)। / \(a_7=32\) and (4d=22), so \(d=\frac{11}{2}\). \(a_{19}=10+16\cdot\frac{11}{2}=98\).

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Question 45/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(18,25,32,\ldots\) में कितने पद (200) से कम हैं?

In the AP \(18,25,32,\ldots\), how many terms are less than (200)?

Explanation opens after your attempt
Correct Answer

D. (27)

Explanation

Simple Explanation

(18+7(n-1)<200) से (7(n-1)<182)। सबसे बड़ा (n=26) है। / From (18+7(n-1)<200), (7(n-1)<182). The greatest (n=26).

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Question 46/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{10}=a+9d=59\) और \(a_{25}=a+24d=149\) है तो \(a_{40}\) क्या होगा?

If \(a_{10}=a+9d=59\) and \(a_{25}=a+24d=149\), what is \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

B. (239)

Explanation

Simple Explanation

(15d=90) से (d=6)। \(a_{40}=149+15\times6=239\)। / From (15d=90), (d=6). \(a_{40}=149+15\times6=239\).

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Question 47/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि AP में \(a_{2}=9\) और \(a_{5}+a_{8}=72\) है तो \(a_{14}\) क्या होगा?

If in an AP \(a_2=9\) and \(a_5+a_8=72\), what is \(a_{14}\)?

Explanation opens after your attempt
Correct Answer

C. (69)

Explanation

Simple Explanation

(a_5+a_8=\(a_2+3d\)+\(a_2+6d\)=18+9d=72) इसलिए (d=6)। \(a_{14}=9+12d=81\)। / (a_5+a_8=\(a_2+3d\)+\(a_2+6d\)=18+9d=72), so (d=6). \(a_{14}=9+12d=81\).

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Question 48/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(-12,-5,2,\ldots\) में (100) से बड़ा पहला पद कौन-सा है?

In the AP \(-12,-5,2,\ldots\), what is the first term greater than (100)?

Explanation opens after your attempt
Correct Answer

B. (103)

Explanation

Simple Explanation

(a_n=-12+7(n-1))। (100) के बाद आने वाला पहला पद (103) है। / (a_n=-12+7(n-1)). The first term after (100) is (103).

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Question 49/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=4n+q\) और \(a_{3n}-a_n=96\) है तो (n) का मान क्या है?

If \(a_n=4n+q\) and \(a_{3n}-a_n=96\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{3n}-a_n=(12n+q)-(4n+q)=8n)। (8n=96) से (n=12)। / (a_{3n}-a_n=(12n+q)-(4n+q)=8n). From (8n=96), (n=12).

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Question 50/50 Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_6=2\) और \(a_{18}=-70\) है। \(a_{30}\) क्या होगा?

In an AP, \(a_6=2\) and \(a_{18}=-70\). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

C. (-142)

Explanation

Simple Explanation

\(d=\frac{-70-2}{18-6}=-6\)। (a_{30}=-70+12(-6)=-142)। / \(d=\frac{-70-2}{18-6}=-6\). (a_{30}=-70+12(-6)=-142).

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