Class 10 Maths · Chapter 5

Arithmetic Progressions

137 Class 10 Maths questions on Arithmetic Progressions from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 7

1. Q21 NCERT · Exercise 5.2
   Find the 20th term from ​the ​last ​term ​of the ​AP : $3,8,13,\dots ,253$.
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   The $20$th term from the last is $158$.

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2. Q22 NCERT · Exercise 5.2
   The ​sum ​of the $4$th ​and $8$th terms of an ​AP is $24$ and the ​sum of the $6$th and $10$th terms is $44$. Find the first ​three ​terms of the ​AP.
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   With $a=-13$ and $d=5$, the first three terms of the AP are $-13,-8,-3$.

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3. Q23 NCERT · Exercise 5.2
   Subba Rao ​started work in ​1995 at an annual salary of Rs ​5000 and received an increment ​of Rs 200 each year. ​In which year did his ​income reach ​Rs 7000?
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   His income reached Rs $7000$ in the year $2005$.

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4. Q24 NCERT · Exercise 5.2
   Ramkali ​saved Rs 5 ​in the ​first ​week ​of a ​year and ​then increased her weekly savings by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.
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   $n=10$: Ramkali's weekly saving becomes Rs $20.75$ in the $10$th week.

   Step-by-step solution →
5. Q25 NCERT · Exercise 5.3
   Find the sum of the following APs: ​

   1. (i)​2, 7, ​12, ..., to 10 terms.
   2. (ii)-37, -33, -29, ..., to 12 ​terms.
   3. (iii)​0.6, 1.7, 2.8, ..., ​to 100 terms.
   4. (iv)1/15, 1/12, ​1/10, ​..., to 11 terms.
   Show answer

   (i) $245$; (ii) $-180$; (iii) $5505$; (iv) $\frac{33}{20}$.

   Step-by-step solution →
6. Q26 NCERT · Exercise 5.3
   Find ​the sums given ​below: ​

   1. (i)$7+10\frac{1}{2}+14+\dots +84$
   2. (ii)$34+32+30+\dots +10$ ​
   3. (iii)$-5+(-8)+(-11)+\dots +(-230)$
   Show answer

   (i) $S_{23}=\frac{2093}{2}=1046\frac{1}{2}$; (ii) $S_{13}=286$; (iii) $S_{76}=-8930$.

   Step-by-step solution →
7. Q27 NCERT · Exercise 5.3
   In ​an ​AP:

   1. (i)given $a=5$, $d=3$, $a_n=50$, find $n$ and $S_n$.
   2. (ii)given $a=7$, $a_{13}=35$, find $d$ and $S_{13}$.
   3. (iii)given $a_{12}=37$, $d=3$, find $a$ ​and $S_{12}$.
   4. (iv)given $a_3=15$, $S_{10}=125$, find $d$ and $a_{10}$.
   5. (v)given $d=5$, $S_9=75$, find $a$ and $a_9$.
   6. (vi)given $a=2$, $d=8$, $S_n=90$, ​find $n$ and $a_n$.
   7. (vii)​given $a=8$, $a_n=62$, $S_n=210$, find $n$ and $d$.
   8. (viii)given $a_n=4$, $d=2$, $S_n=-14$, ​find $n$ and $a$.
   9. (ix)given $a=3$, $n=8$, $S=192$, find $d$.
   10. (x)​given $l=28$, $S=144$, $n=9$, find $a$.
   Show answer

   (i) $n=16,S_{16}=440$; (ii) $d=\frac{7}{3},S_{13}=273$; (iii) $a=4,S_{12}=246$; (iv) $d=-1,a_{10}=8$; (v) $a=-\frac{35}{3},a_9=\frac{85}{3}$; (vi) $n=5,a_n=34$; (vii) $n=6,d=\frac{54}{5}$; (viii) $n=7,a=-8$; (ix) $d=6$; (x) $a=4$.

   Step-by-step solution →
8. Q28 NCERT · Exercise 5.3
   How ​many terms of the AP : $9,17,25,\dots$ must ​be ​taken ​to ​give a sum ​of ​636?
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   $n=12$ terms are needed.

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9. Q29 NCERT · Exercise 5.3
   The first term of ​an AP is 5, ​the last term is ​45 ​and the sum is 400. ​Find the number ​of terms ​and the common difference.
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   $n=16$ and $d=\frac{8}{3}$.

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10. Q30 NCERT · Exercise 5.3
    The first and the last terms of ​an AP ​are $17$ and $350$ ​respectively. If ​the common difference is $9$, ​how many ​terms are there and ​what is their sum?
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    The AP has $n=38$ terms and their sum is $S_{38}=6973$.

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11. Q31 NCERT · Exercise 5.3
    Find the sum of first ​22 terms ​of ​an ​AP in ​which $d=7$ and ​22nd term is 149.
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    $S_{22}=1661$.

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12. Q32 NCERT · Exercise 5.3
    Find ​the sum of first $51$ terms ​of ​an AP ​whose ​second and ​third terms are $14$ ​and $18$ respectively.
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    $S_{51}=5610$.

    Step-by-step solution →
13. Q33 NCERT · Exercise 5.3
    If the sum of first ​7 terms of ​an ​AP is 49 ​and that of ​17 terms is 289, ​find ​the sum of first n terms.
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    $S_n=n^2$ (with $a=1$, $d=2$).

    Step-by-step solution →
14. Q34 NCERT · Exercise 5.3
    Show ​that $a_1,a_2,\dots ,a_n,\dots$ form ​an AP where $a_n$ is ​defined as below. Also find ​the sum ​of ​the first 15 terms ​in each case.

    1. (i)$a_n=3+4n$
    2. (ii)$a_n=9-5n$
    Show answer

    (i) AP with $a=7,d=4$ and $S_{15}=525$. (ii) AP with $a=4,d=-5$ and $S_{15}=-465$.

    Step-by-step solution →
15. Q35 NCERT · Exercise 5.3
    If the sum ​of the first $n$ terms of ​an ​AP is $4n-n^2$, what is the first term ​(that is $S_1$)? What ​is the sum ​of first two terms? What is ​the second term? Similarly, find the 3rd, the 10th and ​the $n$th terms.
    Show answer

    $a_1=3$, $S_2=4$, $a_2=1$, $a_3=-1$, $a_{10}=-15$, and the general term $a_n=5-2n$.

    Step-by-step solution →
16. Q36 NCERT · Exercise 5.3
    Find ​the sum ​of the first ​40 ​positive ​integers divisible ​by ​6.
    Show answer

    $S_{40}=4920$.

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17. Q37 NCERT · Exercise 5.3
    Find ​the ​sum ​of ​the ​first $15$ multiples ​of $8$.
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    $S_{15}=960$.

    Step-by-step solution →
18. Q38 NCERT · Exercise 5.3
    Find ​the sum of ​the ​odd numbers ​between 0 ​and 50.
    Show answer

    The sum of the odd numbers between $0$ and $50$ is $S_{25}=625$.

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19. Q39 NCERT · Exercise 5.3
    A contract on construction job ​specifies a penalty for delay of completion beyond a ​certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the ​third day, ​etc., the penalty ​for each succeeding day being Rs 50 more than for ​the preceding day. How much money the contractor has to pay ​as penalty, if he has delayed the ​work by 30 days?
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    The contractor has to pay a total penalty of Rs $27,750$.

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20. Q40 NCERT · Exercise 5.3
    A sum of $\text{Rs }700$ is ​to be used to give ​seven cash prizes to students of ​a ​school for their overall academic performance. If each prize is $\text{Rs }20$ less than ​its preceding ​prize, find the value ​of each ​of the prizes.
    Show answer

    With $a=160$ and $d=-20$, the seven prizes (in Rs) are $160,140,120,100,80,60,40$.

    Step-by-step solution →