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 14 of 23

1. Q261 CBSE 2023
   The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of ​an A.P. is $2:3$. Find the ratio of the $5^{\text{th}}$ ​term to the $21^{\text{st}}$ term. Also, find the ​ratio ​of ​the sum ​of first ​5 ​terms to the sum of first 21 terms.
   Show answer

   $a_5:a_{21}=1:3$ and $S_5:S_{21}=5:49$

   Step-by-step solution →
2. Q262 CBSE 2023
   If the sum of first 6 terms ​of ​an ​A.P. is 36 and that of the first 16 terms is ​256, ​find the sum of first 10 ​terms.
   Show answer

   $S_{10}=100$

   Step-by-step solution →
3. Q263 CBSE 2023
   If the sum of ​the ​first ​7 terms ​of an A.P. is $-14$ and that ​of 11 ​terms ​is $-55$, ​then find the sum of its first 'n' terms.
   Show answer

   $S_n=\frac{n(13-3n)}{4}$

   Step-by-step solution →
4. Q264 CBSE 2023
   The ratio of the $11^{th}$ term to $17^{th}$ ​term of an ​A.P. is $3:4$. Find the ​ratio ​of $5^{th}$ term to $21^{st}$ term of the same A.P. Also, find the ​ratio of the sum of ​first $5$ terms to that ​of first $21$ ​terms.
   Show answer

   $a_5:a_{21}=3:7$ and $S_5:S_{21}=25:189$.

   Step-by-step solution →
5. Q265 CBSE 2023
   $250$ ​logs are stacked in the following manner ​: $22$ logs ​in the bottom row, $21$ in the ​next row, $20$ in the row next to it and so on ​(as shown ​by an example). In how many rows, are the $250$ logs ​placed and how many logs are there in the ​top row ?

   Show answer

   The logs are placed in $20$ rows, with $3$ logs in the top row.

   Step-by-step solution →
6. Q266 CBSE 2023
   In an ​A.P., the ​sum of the first ​'n' terms is $3n^2+n$. Find the first term and the common ​difference of ​the A.P. ​Hence, ​find its 15th term.
   Show answer

   First term $a=4$, common difference $d=6$, and $a_{15}=88$.

   Step-by-step solution →
7. Q267 CBSE 2023
   Ravindra took a loan of ​Rs 3,45,000 from a ​bank to buy a car, and ​decided to pay back by Rs ​2,000 at the end of the first month and then increased the instalment amount by ​Rs 200 each month. Based on the above, answer the ​following questions :

   1. aFind the amount paid by him in 10th instalment.[1]
   2. bFind the total amount paid by him in first 10 instalments.[1]
   3. cIn how many instalments would he clear his total loan? OR What amount will he be able to clear in his first 45 instalments?[2]
   Show answer

   (a) Rs 3800; (b) Rs 29000; (c) 50 instalments (OR Rs 2,88,000 in 45 instalments).

   Step-by-step solution →
8. Q268 CBSE 2023
   Nikhil started saving money for his new project. He started saving Rs 240 in the first month, Rs 300 ​in the second month, Rs 360 in the third month and so on. ​He continues ​to save ​in this manner for ​quite ​some time. ​Based on ​the above, answer the following questions:

   1. iAre the numbers representing his savings in AP? If so, write the first term $(a)$ and the common difference $(d)$.
   2. iiIn which month will he save Rs $660$?
   3. iii-aWhat amount will he save in the $15^{\text{th}}$ month?
   4. iii-bOR How much money will he accumulate after $10$ months?
   Show answer

   (i) Yes, AP with $a=240$, $d=60$. (ii) 8th month. (iii)(a) Rs 1080. (iii)(b) Rs 5100.

   Step-by-step solution →
9. Q269 CBSE 2023
   Aahana, being a plant lover, decides to convert her balcony into a beautiful garden full of ​plants. ​She ​bought few ​plants with ​pots for her balcony. She placed the pots in such a way that the number of pots in the first ​row is $2$, second row is $5$, third row is $8$, and so ​on. Based on the above information, answer the following ​questions.

   1. (i)Find the number of pots placed in the $10^{th}$ row.[1]
   2. (ii)Find the difference in the number of pots placed in the $5^{th}$ row and the $2^{nd}$ row.[1]
   3. (iii)If Aahana wants to place $100$ pots in total, then find the total number of rows formed in the arrangement.[2]
   4. (iii OR)If Aahana has sufficient space for $12$ rows, then how many total pots are placed by her with the same arrangement?[2]
   Show answer

   (i) $29$ pots; (ii) Difference $9$; (iii) $8$ rows; (iii OR) $222$ pots.

   Step-by-step solution →
10. Q270 CBSE 2023
    A factory ​is manufacturing ​cars and ​is increasing its production by a fixed number ​every year. The factory produced 80,000 cars in the fourth year and ​1,10,000 ​cars in the seventh year. Based on the above, answer the following questions :

    1. aTaking '$a$' as the number of cars produced in the first year and '$d$' the fixed number by which the production is increasing every year, write a relation between '$a$' and '$d$' for the fourth year.[1]
    2. bWrite the relation between '$a$' and '$d$' for the seventh year.[1]
    3. cSolving the above two equations, find '$a$'. (OR) Solving the above two equations, find '$d$'.[2]
    Show answer

    (a) $a+3d=80000$; (b) $a+6d=110000$; (c) $a=50000$ (and $d=10000$).

    Step-by-step solution →
11. Q271 CBSE 2023
    A fashion ​designer is ​designing ​a fabric pattern. In ​each row, ​there ​are some shaded squares and unshaded triangles (see figure). Based on the pattern, answer ​the following questions.

    1. (i)Identify A.P. for the number of squares in each row.[1]
    2. (ii)Identify A.P. for the number of triangles in each row.[1]
    3. (iii)(a)If each shaded square is of side 2 cm, then find the shaded area when 15 rows have been designed.[2]
    4. (iii)(b)OR Write a formula for finding total number of triangles in 'n' number of rows. Hence, find S10.[2]
    Show answer

    (i) Squares: $1,3,5,7,9,\dots$ ($a=1$, $d=2$). (ii) Triangles: $2,6,10,14,18,\dots$ ($a=2$, $d=4$). (iii)(a) $S_{15}=225$ squares, shaded area $=225\times 4=900$ cm${}^2$. (iii)(b) $S_n=2n^2$; $S_{10}=200$.

    Step-by-step solution →
12. Q272 CBSE 2022
    For the A.P. $a_1,a_2,a_3,\dots$ ​if $\frac{a_4}{a_7}=\frac{2}{3}$, then ​find $\frac{a_6}{a_8}$.
    Show answer

    $\frac{a_6}{a_8}=\frac{4}{5}$

    Step-by-step solution →
13. Q273 CBSE 2022
    Find ​the sum ​of first 30 ​terms of ​AP ​: $-30,-24,-18,\dots$
    Show answer

    $S_{30}=1710$

    Step-by-step solution →
14. Q274 CBSE 2022
    In ​an AP, ​if $a=50$, $d=-4$ ​and $S_n=0$, then ​find the value of $n$.
    Show answer

    $n=26$.

    Step-by-step solution →
15. Q275 CBSE 2022
    In ​an AP ​if $S_n=n(4n+1)$, ​then find the ​AP.
    Show answer

    AP is $5,13,21,29,\dots$ (with $a=5$, $d=8$)

    Step-by-step solution →
16. Q276 CBSE 2022
    Find ​the sum of the first ​twelve ​2-digit multiples ​of ​7, using ​an AP.
    Show answer

    The sum of the first twelve 2-digit multiples of 7 is $630$.

    Step-by-step solution →
17. Q277 CBSE 2022
    Find the ​sum of ​first 20 ​terms of an ​AP in ​which $d=5$ ​and $a_{20}=135$.
    Show answer

    $S_{20}=1750$.

    Step-by-step solution →
18. Q278 CBSE 2022
    How ​many natural numbers are there between 1 and 1000 which ​are ​divisible by ​5 but ​not by 2 ​?
    Show answer

    There are $100$ such natural numbers.

    Step-by-step solution →
19. Q279 CBSE 2022
    For an ​AP with common difference $6$, the sum of ​first ten terms ​is same as ​four times the sum of first five terms. Determine ​the first term ​of the AP.
    Show answer

    First term $a=3$

    Step-by-step solution →
20. Q280 CBSE 2022
    Which ​term ​of the ​A.P. $-\frac{11}{2},-3,-\frac{1}{2},\dots$ is $\frac{49}{2}$?
    Show answer

    The $13^{\text{th}}$ term equals $\frac{49}{2}$.

    Step-by-step solution →