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 13 of 23

1. Q241 CBSE 2023
   Which ​term ​of an AP $21,42,63,84,\dots$ ​is $210$ ​?

   1. (a)$12^{\text{th}}$
   2. (b)$11^{\text{th}}$
   3. (c)$10^{\text{th}}$
   4. (d)$9^{\text{th}}$
   Show answer

   (c) $10^{\text{th}}$

   Step-by-step solution →
2. Q242 CBSE 2023
   If $x,2x+9,4x+3$ are ​three ​consecutive terms ​of ​an ​A.P., then ​the ​value ​of $x$ is :

   1. (a)3
   2. (b)10
   3. (c)13
   4. (d)15
   Show answer

   (d) 15

   Step-by-step solution →
3. Q243 CBSE 2023
   The sum ​of the ​first 100 ​even ​natural numbers is ​:

   1. (a)10100
   2. (b)2550
   3. (c)5050
   4. (d)10010
   Show answer

   (a) 10100

   Step-by-step solution →
4. Q244 CBSE 2023
   The $11^{th}$ term from ​the ​end of ​the A.P. ​: $10,7,4,\dots ,-62$ is ​:

   1. (a)25
   2. (b)16
   3. (c)-32
   4. (d)0
   Show answer

   (c) -32

   Step-by-step solution →
5. Q245 CBSE 2023
   If $-5,x,3$ are three ​consecutive ​terms of ​an A.P., then ​the ​value of $x$ ​is

   1. (a)$-2$
   2. (b)$2$
   3. (c)$1$
   4. (d)$-1$
   Show answer

   (d) $-1$

   Step-by-step solution →
6. Q246 CBSE 2023
   If the sum of ​the first $n$ terms of an A.P. be $3n^2+n$ and ​its common ​difference is ​6, then its first ​term is

   1. (a)2
   2. (b)3
   3. (c)1
   4. (d)4
   Show answer

   (d) 4

   Step-by-step solution →
7. Q247 CBSE 2023
   Assertion (A): $a,b,c$ are in A.P. if and only if $2b=a+c$.

   Reason (R): The sum of first $n$ odd natural numbers is $n^2$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer

   (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

   Step-by-step solution →
8. Q248 CBSE 2023
   Find the sum ​of ​the ​first ​15 ​terms ​of the A.P. ​: $\frac{1}{15},\frac{1}{12},\frac{1}{10},\dots$
   Show answer

   $S_{15}=\frac{11}{4}=2\frac{3}{4}$

   Step-by-step solution →
9. Q249 CBSE 2023
   How many terms ​are there ​in an A.P. ​whose ​first ​and fifth terms ​are $-14$ ​and 2, respectively, and the ​last term is 62.
   Show answer

   $n=20$ terms

   Step-by-step solution →
10. Q250 CBSE 2023
    Which ​term of the A.P. : $65,61,57,53,\dots$ ​is ​the first negative ​term ​?
    Show answer

    The 18th term ($a_{18}=-3$) is the first negative term.

    Step-by-step solution →
11. Q251 CBSE 2023
    If $p^{th}$ term of ​an A.P. is $q$ and $q^{th}$ ​term ​is $p$, ​then prove that its $n^{th}$ ​term ​is $(p+q-n)$.
    Show answer

    $a_n=p+q-n$ (proved)

    Step-by-step solution →
12. Q252 CBSE 2023
    Find ​the sum of all ​integers between 50 and ​500, which are ​divisible ​by ​7.
    Show answer

    The sum is $17696$.

    Step-by-step solution →
13. Q253 CBSE 2023
    How many ​numbers lie between 10 ​and 300, which when divided ​by 4 leave ​a remainder 3? ​Also, ​find their sum.
    Show answer

    There are $73$ such numbers and their sum is $11315$.

    Step-by-step solution →
14. Q254 CBSE 2023
    The sum ​of first 9 terms of an AP is 171 and ​the sum of its first ​24 terms ​is ​996. ​Find ​the $20^{\text{th}}$ term of the AP.
    Show answer

    $a_{20}=64$

    Step-by-step solution →
15. Q255 CBSE 2023
    How ​many terms ​of ​the arithmetic progression $45,39,33,\dots$ must be taken ​so ​that their sum is $180$? Explain the double ​answer.
    Show answer

    $n=6$ or $n=10$; the extra terms (from the 8th onward become negative) cancel so both give the sum $180$.

    Step-by-step solution →
16. Q256 CBSE 2023
    Solve ​the equation ​for $x$: $-4+(-1)+2+\dots +x=437$.
    Show answer

    $x=50$ (with $n=19$ terms)

    Step-by-step solution →
17. Q257 CBSE 2023
    The sum of first $n$ terms of ​an AP is $5n^2+3n$. If its $n^{\text{th}}$ term ​is $168$, find $n$. Also, ​find ​the $20^{\text{th}}$ ​term ​of the AP.
    Show answer

    $n=17$; $a_{20}=198$

    Step-by-step solution →
18. Q258 CBSE 2023
    The ​first ​term of ​an A.P. ​is $22$, the last term is $-6$ and the sum of all the ​terms is $64$. Find ​the number ​of terms of ​the A.P. Also, find the common difference.
    Show answer

    $n=8$ terms and common difference $d=-4$

    Step-by-step solution →
19. Q259 CBSE 2023
    Find the sum ​of first $25$ ​terms ​of the A.P. whose $n^{th}$ term is ​given by $a_n=5+6n$. Also, ​find the ​ratio of $20^{th}$ ​term to $45^{th}$ term.
    Show answer

    $S_{25}=2075$; ratio $a_{20}:a_{45}=5:11$.

    Step-by-step solution →
20. Q260 CBSE 2023
    In ​an ​A.P., ​if $S_n=3n^2+5n$ ​and $a_k=164$, ​find ​the value of $k$.
    Show answer

    $k=27$

    Step-by-step solution →