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 18 of 23

1. Q341 CBSE 2020
   The $10^{th}$ term of an ​AP ​is $29$ ​and the sum of ​its first $20$ terms is $610$. Find the sum of ​its ​first $30$ terms.
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   $S_{30}=1365$.

   Step-by-step solution →
2. Q342 CBSE 2020
   The sum of ​the ​first $3$ terms of an ​A.P. is $21$ and the ​sum ​of their squares ​is $155$. Find the ​A.P.
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   The A.P. Is $5,7,9$ (or $9,7,5$ for $d=-2$).

   Step-by-step solution →
3. Q343 CBSE 2019
   Find the ​common ​difference ​of ​the ​Arithmetic Progression (A.P.) $\frac{1}{a},\frac{3-a}{3a},\frac{3-2a}{3a},\dots (a\ne 0)$
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   Common difference $d=-\frac{1}{3}$.

   Step-by-step solution →
4. Q344 CBSE 2019
   Find ​the sum of ​first $10$ multiples ​of $6$.
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   The sum of the first $10$ multiples of $6$ is $330$.

   Step-by-step solution →
5. Q345 CBSE 2019
   If ​in ​an ​A.P., $a=15$, $d=-3$ and $a_n=0$, ​then find ​the ​value of $n$.
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   $n=6$

   Step-by-step solution →
6. Q346 CBSE 2019
   How many ​two ​digits ​numbers are ​divisible by $3$?
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   There are $30$ two-digit numbers divisible by $3$.

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7. Q347 CBSE 2019
   If the first and ​last terms of an A.P. are $1$ and $11$ respectively, ​and ​the sum of all its ​terms ​is $36$, ​find the number ​of terms in the A.P.
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   The A.P. Has $6$ terms.

   Step-by-step solution →
8. Q348 CBSE 2019
   If the ​first term ​of an ​A.P. is $2$ and common ​difference ​is $4$, then ​find the sum of ​its first $40$ terms.
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   The sum of the first $40$ terms is $3200$.

   Step-by-step solution →
9. Q349 CBSE 2019
   Find ​the ​number ​of terms ​in the ​A.P. ​: $18,15\frac{1}{2},13,\dots ,-47$.
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   The A.P. Has $27$ terms.

   Step-by-step solution →
10. Q350 CBSE 2019
    If $S_n$, the ​sum of ​the first $n$ ​terms of ​an ​A.P. is given ​by $S_n=2n^2+n$, then find ​its $n^{th}$ ​term.
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    $a_n=4n-1$

    Step-by-step solution →
11. Q351 CBSE 2019
    If ​the $17^{th}$ ​term ​of ​an ​A.P. exceeds ​its $10^{th}$ term by $7$, find the common ​difference.
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    $d=1$

    Step-by-step solution →
12. Q352 CBSE 2019
    Which ​term of the ​AP $3,15,27,39,\dots$ ​will be $120$ ​more ​than its $21$st term?
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    The $31$st term is $120$ more than the $21$st term.

    Step-by-step solution →
13. Q353 CBSE 2019
    Find ​the $11^{\text{th}}$ ​term from ​the ​last term (towards the first ​term) of ​the A.P. $10,7,4,\dots ,-62$.
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    The $11^{\text{th}}$ term from the last is $-32$.

    Step-by-step solution →
14. Q354 CBSE 2019
    If $S_n$, ​the sum ​of first $n$ ​terms ​of an AP is ​given by $S_n=3n^2-4n$, ​find the $n$th term.
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    $a_n=6n-7$.

    Step-by-step solution →
15. Q355 CBSE 2019
    How ​many $2$-digit ​numbers ​are divisible ​by $7$ ​?
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    There are $13$ two-digit numbers divisible by $7$.

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16. Q356 CBSE 2019
    How ​many ​multiples ​of $4$ ​lie between $10$ ​and $205$?
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    There are $49$ multiples of $4$ between $10$ and $205$.

    Step-by-step solution →
17. Q357 CBSE 2019
    Determine the A.P. ​whose ​third term ​is $16$ and ​the $7^{\text{th}}$ term ​exceeds the $5^{\text{th}}$ ​term by $12$.
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    First term $a=4$, common difference $d=6$; the A.P. Is $4,10,16,22,28,\dots$

    Step-by-step solution →
18. Q358 CBSE 2019
    If the sum of first ​four terms ​of an AP is $40$ and that of ​first $14$ terms ​is $280$. Find ​the ​sum of its ​first $n$ ​terms.
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    $S_n=n^2+6n$ (equivalently $n(n+6)$).

    Step-by-step solution →
19. Q359 CBSE 2019
    If the ​sum of the ​first $p$ terms of an A.P. ​is $q$ and ​the sum of the first $q$ terms is $p$; ​then show that ​the sum of the first $(p+q)$ terms is $\{-(p+q)\}$.
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    $S_{p+q}=-(p+q)$ (proved).

    Step-by-step solution →
20. Q360 CBSE 2019
    Find ​the ​value of $x$, ​when in ​the ​A.P. ​given ​below $2+6+10+\dots +x=1800$.
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    $x=118$.

    Step-by-step solution →