Class 10 Maths · Chapter 5

Arithmetic Progressions

441 Class 10 Maths questions on Arithmetic Progressions from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 6 of 23

1. Q101 Exemplar · Exercise 5.3
   Find the sum ​of first 17 ​terms ​of an ​AP whose $4^{th}$ ​and $9^{th}$ terms are $-15$ ​and $-30$ ​respectively.
   Show answer

   With $a=-6$ and $d=-3$, $S_{17}=\frac{17}{2}(-60)=-510$.

   Step-by-step solution →
2. Q102 Exemplar · Exercise 5.3
   If sum of first 6 terms of an ​AP is 36 and that of ​the first 16 terms is 256, ​find ​the sum of first 10 ​terms.
   Show answer

   The sum of the first 10 terms is $S_{10}=100$ (with $a=1$, $d=2$).

   Step-by-step solution →
3. Q103 Exemplar · Exercise 5.3
   Find ​the sum of ​all the 11 ​terms of an ​AP whose ​middle ​most ​term ​is 30.
   Show answer

   The sum of all 11 terms is $330$.

   Step-by-step solution →
4. Q104 Exemplar · Exercise 5.3
   Find the ​sum of ​last ten ​terms ​of the ​AP: $8,10,12,\dots ,126$.
   Show answer

   The sum of the last ten terms is $1170$.

   Step-by-step solution →
5. Q105 Exemplar · Exercise 5.3
   Find ​the sum of first ​seven numbers ​which ​are multiples of 2 ​as well as of 9. ​[Hint: Take the LCM ​of 2 ​and 9.]
   Show answer

   The seven numbers are $18,36,54,72,90,108,126$ and their sum is $S_7=504$.

   Step-by-step solution →
6. Q106 Exemplar · Exercise 5.3
   How ​many ​terms of the AP: $-15,-13,-11,\dots$ are ​needed ​to ​make the ​sum $-55$? ​Explain the reason for double answer.
   Show answer

   $n=5$ or $n=11$. The double answer occurs because terms $a_6$ to $a_{11}$ (namely $-5,-3,-1,1,3,5$) sum to $0$, so $S_5=S_{11}=-55$.

   Step-by-step solution →
7. Q107 Exemplar · Exercise 5.3
   The sum of the first $n$ terms ​of an AP whose first term is 8 and the common difference is ​20 is equal to ​the sum of first $2n$ terms ​of another AP ​whose first term is $-30$ ​and the common difference is ​8. Find $n$.
   Show answer

   $n=11$.

   Step-by-step solution →
8. Q108 Exemplar · Exercise 5.3
   Kanika ​was given her pocket money on Jan $1^{st}$, $2008$. ​She puts Re $1$ on Day $1$, Rs $2$ on Day $2$, Rs $3$ on Day $3$, and continued doing so till the end of the month, from this money into ​her piggy bank. She also spent Rs $204$ of her pocket money, and found that at the end of ​the ​month she still ​had Rs $100$ with her. How much was ​her pocket money for the month?
   Show answer

   Kanika's pocket money for the month was Rs $800$.

   Step-by-step solution →
9. Q109 Exemplar · Exercise 5.3
   Yasmeen ​saves Rs $32$ during the ​first month, Rs $36$ ​in ​the second month and Rs $40$ ​in the third month. If she continues to ​save in this manner, in how many months will she ​save Rs $2000$?
   Show answer

   Yasmeen will save Rs $2000$ in $25$ months.

   Step-by-step solution →
10. Q110 Exemplar · Exercise 5.4
    The sum of the first five terms of an AP and the ​sum of the first seven ​terms of ​the ​same AP is 167. If the sum of ​the first ​ten terms of this AP is 235, find the ​sum of its first twenty terms.
    Show answer

    $S_{20}=970$ (with $a=1$, $d=5$).

    Step-by-step solution →
11. Q111 Exemplar · Exercise 5.4
    Find the

    1. (i)sum of those integers between 1 and 500 which are multiples of ​2 as well ​as of 5.
    2. (ii)sum of those integers from 1 to 500 which are ​multiples of 2 as well as of 5.
    3. (iii)sum of those ​integers from 1 to 500 ​which are multiples of 2 or 5. [Hint (iii): These numbers will be: multiples of 2 + multiples of 5 - ​multiples of 2 as well as of ​5]

    1. (i)Sum of integers between 1 and 500 that are multiples of 2 as well as of 5.
    2. (ii)Sum of integers from 1 to 500 that are multiples of 2 as well as of 5.
    3. (iii)Sum of integers from 1 to 500 that are multiples of 2 or 5.
    Show answer

    (i) 12250 (ii) 12750 (iii) 75250.

    Step-by-step solution →
12. Q112 Exemplar · Exercise 5.4
    The eighth term of ​an ​AP is half ​its second term and the eleventh ​term exceeds ​one ​third of its fourth term by 1. Find the $15^{\text{th}}$ term.
    Show answer

    The 15th term of the AP is $3$ (with $a=-39$ and $d=3$).

    Step-by-step solution →
13. Q113 Exemplar · Exercise 5.4
    An AP consists of ​37 terms. The ​sum of the three ​middle most terms ​is ​225 ​and ​the sum of the last three is 429. Find the AP.
    Show answer

    The AP is $3,7,11,15,\dots ,147$ (with $a=3$, $d=4$).

    Step-by-step solution →
14. Q114 Exemplar · Exercise 5.4
    Find ​the sum of ​the integers between 100 and 200 that are

    1. (i)divisible ​by ​9
    2. (ii)not divisible by 9. [Hint (ii): These numbers ​will be: ​Total numbers - Total numbers divisible by ​9]

    1. idivisible by 9
    2. iinot divisible by 9
    Show answer

    (i) Sum of multiples of 9 $=1683$; (ii) Sum of integers not divisible by 9 $=14850-1683=13167$.

    Step-by-step solution →
15. Q115 Exemplar · Exercise 5.4
    The ratio of the $11^{th}$ term to the $18^{th}$ term ​of an AP is $2:3$. Find the ratio of the $5^{th}$ ​term to the $21^{st}$ term, and ​also the ratio of the ​sum ​of the first five ​terms to the ​sum of the first $21$ ​terms.
    Show answer

    $a_5:a_{21}=1:3$ and $S_5:S_{21}=5:49$.

    Step-by-step solution →
16. Q116 Exemplar · Exercise 5.4
    Show ​that the sum ​of ​an AP whose ​first term is $a$, the second term $b$ and ​the ​last term $c$, is equal to $\frac{(a+c)(b+c-2a)}{2(b-a)}$.
    Show answer

    $S=\frac{(a+c)(b+c-2a)}{2(b-a)}$, hence proved.

    Step-by-step solution →
17. Q117 Exemplar · Exercise 5.4
    Solve ​the ​equation $-4+(-1)+2+\dots +x=437$.
    Show answer

    $n=19$ and the last term is $x=50$.

    Step-by-step solution →
18. Q118 Exemplar · Exercise 5.4
    Jaspal Singh repays his total loan ​of Rs 118000 by paying ​every month starting with the first instalment ​of Rs 1000. If he increases the instalment by Rs 100 ​every month, what amount will be paid by him in the 30th instalment? What amount of loan does he ​still have ​to pay after the ​30th ​instalment?
    Show answer

    30th instalment $=$ Rs $3900$; loan still to be paid after the 30th instalment $=$ Rs $44500$.

    Step-by-step solution →
19. Q119 Exemplar · Exercise 5.4
    The students of a school decided to beautify the school on the Annual Day by fixing colourful flags ​on the straight passage of the school. They have $27$ flags to be ​fixed at intervals of every $2$ m. The flags are stored at the position ​of the ​middle most flag. Ruchi was ​given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one ​flag at a time. How much distance ​did she cover ​in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
    Show answer

    Total distance covered $=728$ m; maximum distance travelled carrying a flag $=26$ m.

    Step-by-step solution →
20. Q120 CBSE 2026
    The $n^{\text{th}}$ ​term of ​an A.P. is $\sqrt{2}n+1$. ​Its common ​difference ​is ​:

    1. (a)$\sqrt{2}$
    2. (b)$\sqrt{2}n$
    3. (c)$1$
    4. (d)$\sqrt{2}+1$
    Show answer

    (a) $\sqrt{2}$

    Step-by-step solution →