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 15 of 23

1. Q281 CBSE 2022
   Determine the $36^{th}$ term of ​the ​A.P. whose first ​two terms ​are $-3$ and $4$ ​respectively.
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   $a_{36}=242$

   Step-by-step solution →
2. Q282 CBSE 2022
   Which term ​of ​the ​A.P. $3,8,13,18,\dots$ ​is $78$ ​?
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   $78$ is the $16$th term of the A.P.

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3. Q283 CBSE 2022
   Write the ​next ​two ​terms ​of ​the A.P.: $\sqrt{27},\sqrt{48},\sqrt{75},\dots$
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   Next two terms: $\sqrt{108}(=6\sqrt{3})$ and $\sqrt{147}(=7\sqrt{3})$

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4. Q284 CBSE 2022
   Find ​the ​common ​difference ​of an A.P. whose $n^{th}$ ​term ​is given ​by $a_n=6n-5$.
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   Common difference $d=6$.

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5. Q285 CBSE 2022
   Find $a$ ​and $b$ ​so ​that the ​numbers $a,7,b,23$ are in ​A.P.
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   $a=-1$ and $b=15$

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6. Q286 CBSE 2022
   If the ​first term of an A.P. ​is $5$, ​the $n^{th}$ term is $40$ ​and ​the sum ​of first $n$ terms ​is $180$, find the value of $n$.
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   $n=8$

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7. Q287 CBSE 2022
   Find the ​number ​of terms ​of ​the ​A.P. : $293,285,277,\dots ,53$.
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   $n=31$ terms

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8. Q288 CBSE 2022
   Find ​the sum of ​the first 40 positive integers divisible ​by ​7.
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   $S_{40}=5740$

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9. Q289 CBSE 2022
   Find ​the $20^{th}$ term ​of the ​A.P. whose $7^{th}$ term ​is $24$ ​less than the $11^{th}$ term, the first ​term being $12$.
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   $a_{20}=126$

   Step-by-step solution →
10. Q290 CBSE 2022
    The $n^{\text{th}}$ term of a ​sequence ​is given by $a_n=\frac{n(n+1)(2n+1)}{6}$. Write ​the first three ​terms ​of the sequence. Does this sequence ​form an ​A.P. ? Justify ​your answer.
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    First three terms: $1,5,14$. The sequence is **not** an A.P. Because $a_2-a_1=4$ while $a_3-a_2=9$, so the common difference is not constant.

    Step-by-step solution →
11. Q291 CBSE 2022
    For ​what ​value ​of ​'$n$', are ​the $n^{th}$ ​terms of ​the APs : $9,7,5,\dots$ and $15,12,9,\dots$ the same ?
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    $n=7$.

    Step-by-step solution →
12. Q292 CBSE 2022
    Which ​term of ​AP: $\frac{11}{4},\frac{7}{2},\frac{17}{4},\dots$ is $\frac{53}{4}$?
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    The $15$th term

    Step-by-step solution →
13. Q293 CBSE 2022
    Find the sum ​of ​first 20 ​terms ​of an A.P. ​whose $n^{\text{th}}$ ​term ​is given ​as $a_n=5-2n$.
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    $S_{20}=-320$

    Step-by-step solution →
14. Q294 CBSE 2022
    Find the ​sum ​of the ​first ​fifteen multiples ​of $8$.
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    Sum $=960$.

    Step-by-step solution →
15. Q295 CBSE 2022
    Find ​the sum ​of first $16$ ​terms ​of ​the ​A.P. whose $n^{th}$ term is given by $a_n=5n-3$.
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    $S_{16}=632$

    Step-by-step solution →
16. Q296 CBSE 2022
    If the last term of an ​A.P. of 30 terms is 119 ​and the 8th term from ​the end (towards ​the first term) is 91, then ​find the common difference ​of the A.P. Hence, find the sum ​of all the terms of the A.P.
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    Common difference $d=4$ and the sum of all terms is $S_{30}=1830$.

    Step-by-step solution →
17. Q297 CBSE 2022
    Do you know old clothes which are thrown as waste not only ​fill the landfill site but also produce very harmful greenhouse gas. ​So, it is very important that we reuse old clothes in whatever way we can. The picture given shows a footmat (rug) made out of old t-shirts ​yarn. Observing the picture, you ​will notice that ​number of stitches ​in circular rows are making a pattern: 6, 12, 18, 24, ​... Based on the above ​information, answer the following questions using AP.

    1. aCheck whether the given pattern forms an AP. If yes, find the common difference and the next term of the AP.[2]
    2. bWrite the n-th term of the AP. Hence, find the number of stitches in the 10th circular row.[2]
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    (a) Yes, it is an AP with $d=6$; next term $=30$. (b) $a_n=6n$, so the 10th row has $60$ stitches.

    Step-by-step solution →
18. Q298 CBSE 2022
    In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used ​in different figures. One such pattern is ​shown below. ​Observe ​the pattern ​and answer the following questions using ​Arithmetic Progression :

    1. aWrite the AP for the number of triangles used in the figures. Also, write the $n^{th}$ term of this AP.[2]
    2. bWhich figure has 61 matchsticks ?[2]
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    (a) Triangle AP: $4,6,8,\dots$, $a_n=2n+2$. (b) Matchstick AP $12,19,26,\dots$ has $a_n=7n+5$; $7n+5=61\Rightarrow n=8$, so Figure $8$ has $61$ matchsticks.

    Step-by-step solution →
19. Q299 CBSE 2020
    The first term of an A.P. is $5$ ​and ​the last term is $45$. ​If ​the ​sum of all the terms is $400$, the number ​of ​terms is

    1. (a)$20$
    2. (b)$8$
    3. (c)$10$
    4. (d)$16$
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    (d) $16$

    Step-by-step solution →
20. Q300 CBSE 2020
    The $9^{\text{th}}$ ​term ​of ​the A.P. $-15,-11,-7,\dots ,49$ is

    1. (a)32
    2. (b)0
    3. (c)17
    4. (d)13
    Show answer

    (c) 17

    Step-by-step solution →