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 12 of 23

1. Q221 CBSE 2024
   In ​an A.P. ​of $40$ terms, the sum ​of first $9$ terms is $153$ ​and the sum of last $6$ terms is $687$. Determine the ​first term and common difference of A.P. Also, find the sum of ​all the ​terms of the A.P.
   Show answer

   First term $a=5$, common difference $d=3$, and the sum of all the terms $S_{40}=2540$.

   Step-by-step solution →
2. Q222 CBSE 2024
   Find the sum of ​all ​multiples ​of ​9 lying ​between 300 and ​700.
   Show answer

   The sum of all multiples of 9 lying between $300$ and $700$ is $21978$.

   Step-by-step solution →
3. Q223 CBSE 2024
   The $26^{\text{th}}$, $11^{\text{th}}$ ​and the last ​term ​of ​an A.P. are $0$, $3$ and $-\frac{1}{5}$ ​respectively. Find the common difference ​and the ​number ​of terms of the A.P.
   Show answer

   Common difference $d=-\frac{1}{5}$; number of terms $n=27$.

   Step-by-step solution →
4. Q224 CBSE 2024
   A manufacturer ​of TV sets ​produced 720 TV sets in the fourth ​year and 880 TV sets in ​the eighth year. Assuming that the production increases uniformly by a fixed number every year, find the production in ​the tenth year and the total ​production ​in ​the first seven years.
   Show answer

   Production in the tenth year $=960$ TV sets; total production in the first seven years $=5040$ TV sets.

   Step-by-step solution →
5. Q225 CBSE 2024
   Hari ​wants to participate in a 200 m race. ​He can currently run that distance in 51 seconds, and ​with each day of practice, he ​hopes to take 2 seconds less than the previous day. He wants to do it in ​31 seconds. Based on the ​above information, answer the following questions:

   1. (i)Write the A.P. which represents the above situation.
   2. (ii)Find the minimum number of days he needs to practice to achieve the goal. (iii)(a) ​Find the expression ​for the $n^{th}$ term of the A.P. OR (iii)(b) If he wants to do it in 21 seconds, how many minimum days will he take?

   1. iWrite the A.P. which represents the above situation.[1]
   2. iiFind the minimum number of days he needs to practice to achieve the goal.[1]
   3. iii(a)Find the expression for the $n^{th}$ term of the A.P.[2]
   4. iii(b)If he wants to do it in 21 seconds, how many minimum days will he take?[2]
   Show answer

   (i) The A.P. is $51,49,47,45,\dots$ (times in seconds); (ii) He reaches $31$ s on the 11th day, so the minimum number of days is $11$; (iii)(a) $a_n=53-2n$; (iii)(b) $16$ days (the 16th term is $21$).

   Step-by-step solution →
6. Q226 CBSE 2024
   Saving money is ​a good habit and ​it should be inculcated in children ​right from the beginning. Rehan's mother brought a piggy bank for Rehan ​and puts one ₹ 5 coin ​of ​her savings in the piggy bank on the ​first day. She increases his savings by one ₹ 5 coin daily. Based on the above information, ​answer the following questions :

   1. (i)How many coins were added to the piggy bank on $8^{\text{th}}$ day ?[1]
   2. (ii)How much money will be there in the piggy bank after $8$ days?[1]
   3. (iii)(a)If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it.[2]
   4. (iii)(b)OR : Find the total money saved, when the piggy bank is full.[2]
   Show answer

   (i) $8$ coins; (ii) ₹180; (iii)(a) $15$ days; OR (iii)(b) ₹600

   Step-by-step solution →
7. Q227 CBSE 2024
   While preparing for a competitive examination, Akbar came across a match-stick pattern based question. ​The pattern ​is given below. Based ​on the above ​information, answer the following questions :

   1. (i)​Write first term and common difference of the ​A.P. formed by number ​of squares in each figure.
   2. (ii)Write first term and common difference of the A.P. formed by number of sticks ​used in each figure. (iii)(a) How many squares are there in Fig. (10)? Also, write the number of sticks used in Fig. (10). OR (iii)(b) If 88 sticks are used to make $m^{th}$ figure (Fig. (m)), find the value of $m$. How many squares are formed in this figure?

   1. (i)Write first term and common difference of the A.P. formed by number of squares in each figure.[1]
   2. (ii)Write first term and common difference of the A.P. formed by number of sticks used in each figure.[1]
   3. (iii)(a)How many squares are there in Fig. (10)? Also, write the number of sticks used in Fig. (10).[2]
   4. (iii)(b)If 88 sticks are used to make $m^{th}$ figure, find $m$. How many squares are formed in this figure?[2]
   Show answer

   (i) First term $a=1$, common difference $d=4$; (ii) First term $a=4$, common difference $d=12$; (iii)(a) Fig. (10) has $37$ squares and uses $112$ sticks; (iii)(b) $m=8$, and Fig. (8) has $29$ squares.

   Step-by-step solution →
8. Q228 CBSE 2024
   The marathon is a long-distance foot race with a distance of 42.195 km, usually run as a road race, but ​the distance can be covered on ​trail routes. ​The ​marathon can be completed by running or with a run/walk strategy. The marathon was one of the original modern Olympic events in 1896. Neha, a student of class X, wishes ​to participate ​in a marathon. She ​decided to begin her practice by gradually increasing her running ​distance. In the first week, she decided to run 3 km each day and increase the distance by 2 km each week, i.e., in the second week she would run 5 km each day, in the third week she would run 7 km each day and so on.

   1. (i)What distance will Neha cover each day of the $8^{th}$ week of her practice?[1]
   2. (ii)In which week would she be able to run for 45 km each day?[1]
   3. (iii)(a)What is the total distance covered by Neha after 11 weeks, if she practised for 5 days in each week?[2]
   4. (iii)(b)Had she increased the distance by 3 km each week instead of 2 km each week, in how many weeks would she have trained herself to run for 42 km per day?[2]
   Show answer

   (i) $17$ km each day; (ii) The $22$nd week; (iii)(a) $715$ km in all; (iii)(b) $14$ weeks.

   Step-by-step solution →
9. Q229 CBSE 2024
   Sumant's mother started a ​new shoe shop. ​To display the shoes, she ​put 3 pairs ​of ​shoes ​in the 1st row, 5 pairs in the 2nd row, 7 pairs in the ​3rd ​row and so on.

   1. (i)How many pairs of shoes are displayed in the 6th row?[1]
   2. (ii)What is the difference of the pairs of shoes in the 1st row and the 6th row?[1]
   3. (iii)(a)Find the total number of pairs of shoes displayed in the first 15 rows.[2]
   4. (iii)(b)If the pairs of shoes displayed in the 4th row are on sale at Rs 500 each, find the total amount earned if all are sold. (OR)[2]
   Show answer

   (i) $13$ pairs of shoes; (ii) $10$ pairs; (iii)(a) $255$ pairs of shoes; (iii)(b) ₹4500

   Step-by-step solution →
10. Q230 CBSE 2024
    A school has decided to plant some endangered trees ​on $51^{st}$ ​World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each ​succeeding row has ​20 more trees than the previous one. The first ​circular row has 50 trees. Based on the above information, answer the following questions :

    1. (i)How many trees will be planted in the $10^{th}$ row?
    2. (ii)How many more trees will be planted in the $8^{th}$ row than in the $5^{th}$ row? (iii)(a) If 3200 trees are to be planted in the park, then how many rows are ​required? OR (iii)(b) ​If ​3200 trees are to be planted in the park, then how many trees are still left to be planted after the $11^{th}$ row?

    1. (i)How many trees will be planted in the 10th row?[1]
    2. (ii)How many more trees will be planted in the 8th row than in the 5th row?[1]
    3. (iii)(a)If 3200 trees are to be planted, how many rows are required?[2]
    4. (iii)(b)OR If 3200 trees are to be planted, how many trees are left after the 11th row?[2]
    Show answer

    (i) $230$ trees are planted in the $10^{\text{th}}$ row; (ii) The $8^{\text{th}}$ row has $60$ more trees than the $5^{\text{th}}$ row; (iii)(a) $16$ rows are required; (iii)(b) $1550$ trees are still left to be planted after the $11^{\text{th}}$ row.

    Step-by-step solution →
11. Q231 CBSE 2024
    Treasure Hunt is an exciting and adventurous game where participants follow a series of ​clues/numbers/maps to discover hidden treasures. Players engage in ​a thrilling quest, solving puzzles and riddles to unveil the location of ​the coveted prize. While playing a treasure hunt ​game, some clues (numbers) are hidden in various spots ​collectively forming an A.P. If the number on the $n^{\text{th}}$ ​spot is $20+4n$, then answer the following questions to help the players in spotting the ​clues.

    1. (i)Which number is on the first spot ?[1]
    2. (ii)(a)Which spot is numbered as $112$ ?[2]
    3. (ii)(b)What is the sum of all the numbers on the first $10$ spots ? (OR)[2]
    4. (iii)Which number is on the $(n-2{)}^{\text{th}}$ spot ?[1]
    Show answer

    (i) The first spot carries the number $24$; (ii)(a) The number $112$ is on the $23^{\text{rd}}$ spot; (ii)(b) The sum of the numbers on the first $10$ spots is $420$; (iii) The $(n-2{)}^{\text{th}}$ spot carries the number $4n+12$.

    Step-by-step solution →
12. Q232 CBSE 2024
    A road roller is a compactor-type engineering vehicle, used ​to compact soil, gravel, concrete, etc, in the construction of roads and foundations. They ​are also used at ​landfills or in agriculture. A company started ​making road rollers 10 years ago and increased its production uniformly by a ​fixed number every year. The company produces ​800 rollers in the $6^{th}$ year ​and 1130 ​rollers in the $9^{th}$ year. Based on the above information, answer the following questions :

    1. (i)What is the company's production in the first year?[1]
    2. (ii)What was the increase in the company's production every year?[1]
    3. (iii)(a)What was the company's production in the 8th year?[2]
    4. (iii)(b)OR What was the company's total production in the first 6 years?[2]
    Show answer

    (i) The first-year production is $250$ rollers; (ii) The production increased by $110$ rollers every year; (iii)(a) The 8th-year production was $1020$ rollers; OR (iii)(b) The total production in the first 6 years was $3150$ rollers.

    Step-by-step solution →
13. Q233 CBSE 2023
    If common difference ​of an ​A.P. is $-6$, ​then ​value of $a_{20}-a_{14}$ ​is:

    1. (a)36
    2. (b)6
    3. (c)$-36$
    4. (d)$-6$
    Show answer

    (c) $-36$

    Step-by-step solution →
14. Q234 CBSE 2023
    The $8^{th}$ term ​of an A.P. is 17 ​and ​its $14^{th}$ ​term is 29. The common difference ​of ​this A.P. is ​:

    1. (a)3
    2. (b)2
    3. (c)5
    4. (d)$-2$
    Show answer

    (b) 2

    Step-by-step solution →
15. Q235 CBSE 2023
    How ​many terms ​are ​there ​in the ​A.P. given below ​? $14,19,24,29,....,119$

    1. (a)18
    2. (b)14
    3. (c)22
    4. (d)21
    Show answer

    (c) 22

    Step-by-step solution →
16. Q236 CBSE 2023
    The ​next term of ​the ​A.P. : $\sqrt{6},\sqrt{24},\sqrt{54}$ ​is ​:

    1. (a)$\sqrt{60}$
    2. (b)$\sqrt{96}$
    3. (c)$\sqrt{72}$
    4. (d)$\sqrt{216}$
    Show answer

    (b) $\sqrt{96}$

    Step-by-step solution →
17. Q237 CBSE 2023
    If $p-1$, $p+1$ and $2p+3$ ​are ​in ​A.P., ​then the ​value ​of $p$ is

    1. (a)$-2$
    2. (b)4
    3. (c)0
    4. (d)2
    Show answer

    (c) 0

    Step-by-step solution →
18. Q238 CBSE 2023
    The common difference ​of ​the ​A.P. whose $n^{th}$ ​term ​is ​given ​by $a_n=3n+7$, is :

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

    (b) 3

    Step-by-step solution →
19. Q239 CBSE 2023
    The ​seventh term ​of ​an ​A.P. whose ​first ​term is $28$ and ​common difference $-4$, is

    1. (a)$0$
    2. (b)$4$
    3. (c)$52$
    4. (d)$56$
    Show answer

    (b) $4$

    Step-by-step solution →
20. Q240 CBSE 2023
    The $4^{\text{th}}$ term from ​the ​end of ​an ​AP $-11,-8,-5,\dots ,49$ ​is:

    1. (a)$40$
    2. (b)$37$
    3. (c)$43$
    4. (d)$58$
    Show answer

    (a) $40$

    Step-by-step solution →