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 19 of 23

1. Q361 CBSE 2019
   If $m$ times the $m^{th}$ term of an Arithmetic Progression is ​equal to $n$ ​times ​its $n^{th}$ term ​and $m\ne n$, ​show that ​the $(m+n{)}^{th}$ ​term of the A.P. is zero.
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   Since $(m-n)\ne 0$, we get $a+(m+n-1)d=0$, i.e. $t_{m+n}=0$. Hence proved.

   Step-by-step solution →
2. Q362 CBSE 2019
   The sum of ​the ​first three ​numbers in an ​Arithmetic ​Progression is $18$. If the ​product ​of the first and the third term is $5$ times the common difference, find the three ​numbers.
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   The three numbers are $2,6,10$ (when $d=4$) or $15,6,-3$ (when $d=-9$).

   Step-by-step solution →
3. Q363 CBSE 2019
   In a flower bed, there ​are $23$ rose plants in the first row, $21$ in the second, $19$ in the ​third, and so on. If there are $5$ rose plants in ​the ​last row, how many rows ​are ​there in the ​flower-bed?
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   There are $10$ rows in the flower-bed.

   Step-by-step solution →
4. Q364 CBSE 2019
   Find ​the common difference of ​an A.P. whose first ​term is $5$ ​and the sum of ​the first four ​terms is half the ​sum of ​its next four terms.
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   The common difference is $d=2$.

   Step-by-step solution →
5. Q365 CBSE 2019
   Which term of the ​Arithmetic ​Progression $-7,-12,-17,-22,\dots$ ​will ​be $-82$? ​Is $-100$ any term of ​the A.P.? ​Give reason for your answer.
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   $-82$ is the 16th term. $-100$ is **not** a term of the AP, because solving $a_n=-100$ gives $n=19.6$, which is not a positive integer.

   Step-by-step solution →
6. Q366 CBSE 2019
   How many ​terms ​of ​the ​Arithmetic ​Progression $45,39,33,\dots$ must be taken so that ​their sum is $180$? Explain ​the double answer.
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   $n=6$ or $n=10$. The double answer arises because terms $7$ to $10$ (which are $9,3,-3,-9$) add up to $0$, so the sum after $10$ terms equals the sum after $6$ terms, namely $180$.

   Step-by-step solution →
7. Q367 CBSE 2018
   Write ​the $m^{\text{th}}$ ​term of ​the ​A.P. $\frac{1}{k},\frac{1+k}{k},\frac{1+2k}{k},\dots$
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   $a_m=\frac{1+(m-1)k}{k}$

   Step-by-step solution →
8. Q368 CBSE 2018
   In an AP, if the ​common difference $(d)=-4$, ​and ​the ​seventh ​term $(a_7)$ ​is $4$, then find the first term.
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   The first term is $a=28$.

   Step-by-step solution →
9. Q369 CBSE 2018
   The $5^{\text{th}}$ ​and $15^{\text{th}}$ terms of an A.P. ​are $13$ ​and $-17$ ​respectively. Find the ​sum ​of first $21$ terms ​of the A.P.
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   $S_{21}=-105$

   Step-by-step solution →
10. Q370 CBSE 2018
    Find the ​sum of ​first $8$ ​multiples ​of $3$.
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    Sum of the first 8 multiples of 3 $=108$.

    Step-by-step solution →
11. Q371 CBSE 2018
    Find ​the ​sum of ​first ​8 ​multiples of 3.
    Show answer

    The sum of the first 8 multiples of 3 is $108$.

    Step-by-step solution →
12. Q372 CBSE 2018
    The sum of four consecutive ​numbers in ​an AP is $32$ ​and the ratio of the product of ​the first and ​the last term to the product of ​two middle terms is $7:15$. Find the numbers.
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    The four numbers are $2,6,10,14$.

    Step-by-step solution →
13. Q373 CBSE 2018
    The sum of ​the ​first $n$ terms of an ​A.P. ​is $5n^2+3n$. ​If its $m^{\text{th}}$ ​term ​is $168$, find the value of $m$. Also find the $20^{\text{th}}$ term of the A.P.
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    $m=17$ and the 20th term $a_{20}=198$.

    Step-by-step solution →
14. Q374 CBSE 2018
    The $4^{\text{th}}$ ​and the last terms of ​an ​A.P. are $11$ ​and $89$ respectively. If there are $30$ terms in ​the ​A.P., find the A.P. and its $23^{\text{rd}}$ term.
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    A.P. Is $2,5,8,11,\dots$ (with $a=2$, $d=3$); the 23rd term is $68$.

    Step-by-step solution →
15. Q375 CBSE 2018
    The ​sum of four ​consecutive numbers in an AP ​is 32 and the ratio of ​the product of ​the first and the last ​term to ​the product ​of two middle terms is $7:15$. Find the numbers.
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    The four numbers are $2,6,10,14$ (or $14,10,6,2$).

    Step-by-step solution →
16. Q376 CBSE 2017
    What ​is ​the ​common ​difference of an ​A.P. in ​which $a_{21}-a_7=84$?
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    The common difference is $d=6$.

    Step-by-step solution →
17. Q377 CBSE 2017
    What ​is the ​common ​difference of an ​A.P. ​in which $a_{21}-a_7=84$?
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    The common difference is $d=6$.

    Step-by-step solution →
18. Q378 CBSE 2017
    Which ​term ​of ​the progression $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4},\dots$ ​is the first ​negative term?
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    The $28$th term ($a_{28}=-\frac{1}{4}$) is the first negative term.

    Step-by-step solution →
19. Q379 CBSE 2017
    Find ​how ​many ​two-digit ​natural numbers are ​divisible ​by $3$.
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    There are $30$ two-digit natural numbers divisible by $3$.

    Step-by-step solution →
20. Q380 CBSE 2017
    If seven ​times ​the $7^{\text{th}}$ term of an A.P. is ​equal to eleven times the $11^{\text{th}}$ ​term, then ​what will ​be its $18^{\text{th}}$ ​term?
    Show answer

    The $18^{\text{th}}$ term is $a_{18}=0$.

    Step-by-step solution →