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 16 of 23

1. Q301 CBSE 2020
   The common ​difference of an ​AP, whose $n^{\text{th}}$ ​term ​is $a_n=(3n+7)$, ​is

   1. (a)$3$
   2. (b)$7$
   3. (c)$10$
   4. (d)$6$
   Show answer

   (a) $3$

   Step-by-step solution →
2. Q302 CBSE 2020
   Which of the ​following ​is $not$ ​an ​A.P. ​?

   1. (a)$-1.2,0.8,2.8,\dots$
   2. (b)$3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2},\dots$
   3. (c)$\frac{4}{3},\frac{7}{3},\frac{9}{3},\frac{12}{3},\dots$
   4. (d)$\frac{-1}{5},\frac{-2}{5},\frac{-3}{5},\dots$
   Show answer

   (c) $\frac{4}{3},\frac{7}{3},\frac{9}{3},\frac{12}{3},\dots$

   Step-by-step solution →
3. Q303 CBSE 2020
   The ​common ​difference ​of ​the ​A.P. $\frac{1}{p},\frac{1-p}{p},\frac{1-2p}{p},\dots$ is

   1. (a)$1$
   2. (b)$\frac{1}{p}$
   3. (c)$-1$
   4. (d)$-\frac{1}{p}$
   Show answer

   (c) $-1$

   Step-by-step solution →
4. Q304 CBSE 2020
   The value of $x$ for ​which $2x$, $(x+10)$ ​and $(3x+2)$ are ​the ​three consecutive ​terms ​of ​an AP, is

   1. (a)$6$
   2. (b)$-6$
   3. (c)$18$
   4. (d)$-18$
   Show answer

   (a) $6$

   Step-by-step solution →
5. Q305 CBSE 2020
   The ​value ​of $p$ ​for which $(2p+1)$, $10$ ​and $(5p+5)$ are ​three ​consecutive terms of an ​AP ​is

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

   (d) $2$

   Step-by-step solution →
6. Q306 CBSE 2020
   The ​number ​of ​terms ​of an ​AP $5,9,13,\dots ,185$ is

   1. (a)$31$
   2. (b)$51$
   3. (c)$41$
   4. (d)$40$
   Show answer

   CBSE awarded this mark to every candidate. The AP $5,9,13,\dots ,185$ has $n=\frac{185-5}{4}+1=46$ terms, and $46$ is not among the printed options — the misprint is in the original 2020 question paper, which the portal reproduces faithfully. The official marking scheme for set 30/3/1 records: "1 mark should be given to each candidate."

   Step-by-step solution →
7. Q307 CBSE 2020
   The ​first term of an AP ​is $p$ and the ​common ​difference is $q$, then its $10^{\text{th}}$ ​term ​is

   1. (a)$q+9p$
   2. (b)$p-9q$
   3. (c)$p+9q$
   4. (d)$2p+9q$
   Show answer

   (c) $p+9q$

   Step-by-step solution →
8. Q308 CBSE 2020
   The $n^{\text{th}}$ ​term ​of the ​A.P. $a,3a,5a,\dots \dots$ is

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

   (b) $(2n-1)a$

   Step-by-step solution →
9. Q309 CBSE 2020
   The second term from ​the end ​of ​the A.P. $5,8,11,\dots ,47$ ​is

   1. (a)50
   2. (b)45
   3. (c)44
   4. (d)41
   Show answer

   (c) 44

   Step-by-step solution →
10. Q310 CBSE 2020
    If $5$, $b$, $c$, $14$ are the ​consecutive ​terms ​of ​an ​A.P., then $b+c=$ ​____.
    Show answer

    $b+c=19$

    Step-by-step solution →
11. Q311 CBSE 2020
    The ​next ​term ​of A.P. $\frac{1}{p},\frac{1-p}{p},\frac{1-2p}{p},\dots$ ​is ​________.
    Show answer

    The next term is $\frac{1-3p}{p}$.

    Step-by-step solution →
12. Q312 CBSE 2020
    Write ​the $26^{\text{th}}$ ​term of ​the ​A.P. $7,4,1,-2,\dots$ ​.
    Show answer

    $a_{26}=-68$.

    Step-by-step solution →
13. Q313 CBSE 2020
    Find ​the ​sum ​of ​the first $100$ natural numbers.
    Show answer

    The sum of the first $100$ natural numbers is $5050$.

    Step-by-step solution →
14. Q314 CBSE 2020
    If $a-b$, $k$, $a+b$ and $x$ ​are four consecutive terms ​of an ​A.P., then ​find the ratio ​between $k$ and $x$ in ​terms of $a$ ​and $b$.
    Show answer

    $k:x=a:(a+2b)$

    Step-by-step solution →
15. Q315 CBSE 2020
    Find the ​common ​difference of the A.P. whose third term ​is $8$ ​and the seventh ​term ​is $20$.
    Show answer

    The common difference is $d=3$.

    Step-by-step solution →
16. Q316 CBSE 2020
    If $3y-1$, $3y+5$ ​and $5y+1$ are ​three ​consecutive terms of an A.P., ​then ​find ​the value of $y$.
    Show answer

    $y=5$

    Step-by-step solution →
17. Q317 CBSE 2020
    The $n$th ​term of ​an ​AP is $(7-4n)$, then what is ​its ​common difference?
    Show answer

    The common difference is $d=-4$.

    Step-by-step solution →
18. Q318 CBSE 2020
    If $3k-2$, $4k-6$ and $k+2$ ​are three consecutive ​terms ​of ​A.P., then find ​the value ​of $k$.
    Show answer

    $k=3$.

    Step-by-step solution →
19. Q319 CBSE 2020
    What ​is ​the ​arithmetic mean of first $n$ ​natural ​numbers?
    Show answer

    $\frac{n+1}{2}$

    Step-by-step solution →
20. Q320 CBSE 2020
    Show that $(a-b{)}^2$, $(a^2+b^2)$ ​and $(a+b{)}^2$ ​are ​in ​AP.
    Show answer

    Since $t_2-t_1=t_3-t_2=2ab$, the terms $(a-b{)}^2$, $(a^2+b^2)$, $(a+b{)}^2$ are in AP with common difference $2ab$.

    Step-by-step solution →