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 10 of 23

1. Q181 CBSE 2025
   Case Study - 1: A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of ​rounds around a track, with each round ​being 300 metres. To make the event more ​challenging and engaging, the organizers planned to increase the distance of each subsequent ​round by 50 metres. For example, the second round will be 350 metres, ​the third round will be ​400 metres and so on. The total number of rounds planned is 10. Based on the information ​given ​above, answer the following questions.

   1. (i)Write the fourth, fifth and sixth term of the Arithmetic Progression so formed.[1]
   2. (ii)Determine the distance of the 8th round.[1]
   3. (iii)(a)Find the total distance run after completing all 10 rounds.[2]
   4. (iii)(b)OR — If a runner completes only the first 6 rounds, what is the total distance run by the runner?[2]
   Show answer

   (i) The fourth, fifth and sixth terms are $450$ m, $500$ m and $550$ m; (ii) The eighth round is $650$ m long; (iii)(a) The total distance run in all $10$ rounds is $5250$ m; (iii)(b) The total distance run in the first $6$ rounds is $2550$ m.

   Step-by-step solution →
2. Q182 CBSE 2025
   To inculcate ​the ​good habit of ​savings in her children, Reema ​brought a ​piggy bank and after putting a $\text{₹}10$ coin ​in it, she handed it over to her daughter Amisha and ​asked as to put money in it from her pocket money at the beginning of every week. Amisha ​put two ten rupee coins at the beginning of next (second) week and in this way increases her savings by one $\text{₹}10$ coin every week. Based on the above, answer the following questions.

   1. (a)How many coins were added in the piggy bank at the beginning of $5^{th}$ week?[1]
   2. (b)How many $\text{₹}10$ coins will be there in the piggy bank after the end of $7$ weeks?[1]
   3. (c)(i)If the piggy bank can hold a maximum of $300\text{₹}10$ coins, after how many weeks it would be full?[2]
   4. (c)(ii)OR — Find the total amount of money in the piggy bank at the end of $20$ weeks.[2]
   Show answer

   (a) $5$ coins were added at the beginning of the fifth week; (b) There will be $28$ coins after the end of $7$ weeks; (c)(i) The piggy bank will be full after $24$ weeks; (c)(ii) It will hold ₹$2100$ at the end of $20$ weeks.

   Step-by-step solution →
3. Q183 CBSE 2025
   In the month of ​September, villagers of Ankurhut ​were falling ill with high temperature. Paracetamol was one of the highest ​sold medicines during that phase. A ​survey was conducted to estimate ​the overall sale of Paracetamol of each pharmacy during the last 7 days. It was observed ​that the number of Paracetamol sold in different shops were all 3-digit numbers, divisible by 13, taken ​in order.

   1. (i)How many Paracetamols were sold by the 7th pharmacy?[1]
   2. (ii)What was the difference between the number of Paracetamols sold by the 14th and the 9th pharmacy?[1]
   3. (iii)(a)How many Paracetamols were sold by the 9th pharmacy from the last?[2]
   4. (iii)(b) ORWhat was the total number of Paracetamols sold in that week?[2]
   Show answer

   (i) The 7th pharmacy sold $182$ Paracetamols; (ii) The difference is $65$ Paracetamols; (iii)(a) The 9th pharmacy from the last sold $884$ Paracetamols; (iii)(b) The total sold in that week is $37674$ Paracetamols.

   Step-by-step solution →
4. Q184 CBSE 2025
   In an equilateral triangle of ​side ​10 cm, equilateral triangles of side 1 cm are formed as shown in the figure below, such that there ​is one ​triangle in the first row, three triangles in the second row, five triangles in the third ​row and so on. Based ​on given information, answer the following questions using Arithmetic ​Progression.

   1. (i)How many triangles will be there in bottom most row?[1]
   2. (ii)How many triangles will be there in fourth row from the bottom?[1]
   3. (iii) (a)Find the total number of triangles of side 1 cm each till 8th row.[2]
   4. (iii) (b)OR — How many more number of triangles are there from 5th row to 10th row than in first 4 rows? Show working.[2]
   Show answer

   (i) The bottom-most row has $19$ triangles; (ii) The fourth row from the bottom has $13$ triangles; (iii)(a) There are $64$ triangles of side $1$ cm till the eighth row; (iii)(b) Rows $5$ to $10$ have $68$ more triangles than the first four rows.

   Step-by-step solution →
5. Q185 CBSE 2025
   In a ​charming village, there ​is a street called 'Maplewood Avenue', where the houses are ​numbered from $1$ to $49$. A ​community group has decided to undertake ​a green renovation project, aiming to install solar panels on ​the houses. They ​have a few questions ​before they begin the project.

   1. (i)How many houses are there on 'Maplewood Avenue'?[1]
   2. (ii)The house numbers follow an Arithmetic Progression. What is the first term of the A.P. and the common difference?[1]
   3. (iii)(a)If the group wanted to calculate the sum of all house numbers from $1$ to $49$, how much would that be?[2]
   4. (iii)(b)What is the sum of the house numbers between $15$ and $30$? (OR alternative to (iii)(a))[2]
   Show answer

   (i) There are $49$ houses; (ii) First term $a=1$, common difference $d=1$; (iii)(a) The sum of all house numbers from $1$ to $49$ is $1225$; (iii)(b) The sum of the house numbers between $15$ and $30$ (houses $16$ to $29$) is $315$.

   Step-by-step solution →
6. Q186 CBSE 2025
   In ​order to organise Annual Sports Day, ​a school prepared an ​eight lane running track with an integrated football field inside the track area as shown in the figure. The length of the innermost lane of the ​track is $400$ m and ​each ​subsequent lane ​is $7.6$ m longer than ​the preceding lane. Based on the given information, answer the following questions, using the concept of Arithmetic Progression.

   1. (i)What is the length of the 6th lane?[1]
   2. (ii)How long is the 8th lane than that of the 4th lane?[1]
   3. (iii)(a)While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student.[2]
   4. (iii)(b)OR — A student took one round each in lane 4 to lane 8. Find the total distance covered by the student.[2]
   Show answer

   (i) The length of the 6th lane is $438$ m; (ii) The 8th lane is $30.4$ m longer than the 4th lane; (iii)(a) The total distance covered in the first six lanes is $2514$ m; (iii)(b) The total distance covered in lanes $4$ to $8$ is $2190$ m.

   Step-by-step solution →
7. Q187 CBSE 2025
   In a garden, saplings ​of rose flowers were planted at equal intervals to form a spiral ​pattern. The spiral is made up of successive semicircles, with centres ​alternatively at A and B, starting with ​centre ​at A, of radii 50 cm, 100 cm, 150 cm, ... as shown in ​the figure given below. Spiral 1 has 10 flowers, Spiral ​2 has 20 flowers, Spiral 3 has 30 flowers and so on. ​Based on the above information, answer the following questions :

   1. iWhat is the radius of the 13th spiral?[1]
   2. iiIf the radius of the nth spiral is 500 cm, find the value of $n$.[1]
   3. iii (a)Find the total number of saplings till the 11th spiral.[2]
   4. iii (b)Till which spiral, will there be a total of 450 saplings?[2]
   Show answer

   (i) The radius of the 13th spiral is $650$ cm; (ii) $n=10$; (iii)(a) The total number of saplings till the 11th spiral is $660$; (iii)(b) There will be a total of $450$ saplings till the 9th spiral.

   Step-by-step solution →
8. Q188 CBSE 2025
   A woman borrowed ​Rs ​10,00,000 from her friend ​and ​promised to return ​the ​borrowed money in monthly instalments beginning ​from ​the next month. After one month, she returned Rs 10,000, the next month she returned Rs 15,000, the third month she returned Rs 20,000 and so on, thereby increasing the monthly instalment uniformly.

   1. (i)Find the amount of instalment paid in the tenth month.[1]
   2. (ii)In which instalment did she pay Rs 40,000 ?[1]
   3. (iii)(a)If she returned Rs 11,50,000 in all, how many instalments did she pay ?[2]
   4. (iii)(b)By which instalment has she returned a total amount of Rs 3,25,000 ?[2]
   Show answer

   (i) The tenth instalment is ₹55,000; (ii) She paid ₹40,000 in the 7th instalment; (iii)(a) She paid 20 instalments; (iii)(b) She had returned ₹3,25,000 by the 10th instalment.

   Step-by-step solution →
9. Q189 CBSE 2025
   Cable cars at hill stations are ​one ​of the major tourist attractions. ​On a hill station, the length of cable ​car ride from base point to top most point on the hill ​is $5,000$ m. Poles are installed at equal intervals on the way to provide support to the cables on which the cars travel. The distance of first pole from base point is $200$ m and ​subsequent poles are installed at an ​interval of $150$ m. Further, the distance of last pole from the top is $300$ m. Based ​on above information, answer the following questions using Arithmetic Progression.

   1. (i)Find the distance of $10^{\text{th}}$ pole from the base.[1]
   2. (ii)Find the distance between $15^{\text{th}}$ pole and $25^{\text{th}}$ pole.[1]
   3. (iii)(a)Find the time taken by cable car to reach $15^{\text{th}}$ pole from the top if it is moving at the speed of $5$ m/sec and coming down from top.[2]
   4. (iii)(b)OR — Find the total number of poles installed along the entire journey.[2]
   Show answer

   (i) The 10th pole is $1550$ m from the base; (ii) The 15th and 25th poles are $1500$ m apart; (iii)(a) The car takes $480$ s ($8$ minutes) to reach the 15th pole from the top; (iii)(b) There are $31$ poles in all.

   Step-by-step solution →
10. Q190 CBSE 2025
    A long passenger train has $72$ passengers in the ​first coach, $68$ passengers ​in the second coach, $64$ passengers in the ​third coach and ​so on. Based on the above ​information, answer the following ​questions:

    1. (i)If the number of passengers in the successive coaches form an AP, then find the first term and the common difference of the AP.[1]
    2. (ii)In which coach is the number of passengers $56$?[1]
    3. (iii)(a)How many passengers are there in total, in the first $10$ coaches?[2]
    4. (iii)(b)How many passengers are there in the $10^{th}$ coach?[2]
    Show answer

    (i) First term $a=72$, common difference $d=-4$; (ii) The $5^{th}$ coach; (iii)(a) $540$ passengers; (iii)(b) $36$ passengers.

    Step-by-step solution →
11. Q191 CBSE 2025
    A tent house owner provides furniture on rent. He stacks chairs in his shop to save space. In the diagram, ​the height ​of seat ​of chair from ground is represented by $h_1,h_2,h_3,h_4,\dots$ The ​height of ​first seat is 44 cm ​from ground level and gap between every two seats ​is 10 ​cm.

    1. (i)Write the values of $h_1,h_2,h_3,h_4$ and $h_5$ in this order only.[1]
    2. (ii)Show that the above values form an A.P. Write its first term and common difference.[1]
    3. (iii)(a)If chairs can be stacked up to the maximum height of 160 cm, then find the maximum number of chairs in a stack.[2]
    4. (iii)(b)OR Is it possible to stack 15 chairs if maximum height of the stack can not be more than 180 cm? Justify your answer.[2]
    Show answer

    (i) $h_1=44$ cm, $h_2=54$ cm, $h_3=64$ cm, $h_4=74$ cm, $h_5=84$ cm; (ii) Each height is $10$ cm more than the one before it, so the heights form an A.P. with first term $a=44$ cm and common difference $d=10$ cm; (iii)(a) At most $12$ chairs can be stacked; (iii)(b) No, it is not possible: the $15$th seat would be at $h_{15}=184$ cm, which is more than $180$ cm.

    Step-by-step solution →
12. Q192 CBSE 2024
    If 5 times ​the $5^{th}$ term of ​an ​A.P. ​is equal to 9 times ​the $9^{th}$ term, ​then its $14^{th}$ term ​is:

    1. (a)5
    2. (b)9
    3. (c)0
    4. (d)14
    Show answer

    (c) 0

    Step-by-step solution →
13. Q193 CBSE 2024
    The ​next ​($4^{\text{th}}$) term ​of ​the ​A.P. $\sqrt{18},\sqrt{50},\sqrt{98},\dots$ is :

    1. (a)$\sqrt{128}$
    2. (b)$\sqrt{140}$
    3. (c)$\sqrt{162}$
    4. (d)$\sqrt{200}$
    Show answer

    (c) $\sqrt{162}$

    Step-by-step solution →
14. Q194 CBSE 2024
    In ​an ​A.P., if $a=8$ and $a_{10}=-19$, then ​value ​of $d$ ​is:

    1. (a)$3$
    2. (b)$-\frac{11}{9}$
    3. (c)$-\frac{27}{10}$
    4. (d)$-3$
    Show answer

    (d) $-3$

    Step-by-step solution →
15. Q195 CBSE 2024
    The ​common ​difference of ​the ​A.P. $\frac{1}{2x},\frac{1-4x}{2x},\frac{1-8x}{2x},\dots$ is :

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

    (b) $-2$

    Step-by-step solution →
16. Q196 CBSE 2024
    The ​common ​difference of ​an A.P. ​in which $a_{15}-a_{11}=48$, ​is

    1. (a)$12$
    2. (b)$16$
    3. (c)$-12$
    4. (d)$-16$
    Show answer

    (a) $12$

    Step-by-step solution →
17. Q197 CBSE 2024
    If $k+7$, $2k-2$ and $2k+6$ are ​three consecutive ​terms of an ​A.P., then ​the value of $k$ ​is :

    1. (a)$15$
    2. (b)$17$
    3. (c)$5$
    4. (d)$1$
    Show answer

    (b) $17$

    Step-by-step solution →
18. Q198 CBSE 2024
    In ​an A.P., if $d=-4$ and $a_7=4$, then ​the ​first ​term $a$ is ​equal ​to

    1. (a)$6$
    2. (b)$7$
    3. (c)$20$
    4. (d)$28$
    Show answer

    (d) $28$

    Step-by-step solution →
19. Q199 CBSE 2024
    In an A.P., if the first ​term $a=7$, $n$th term $a_n=84$ and ​the ​sum of ​first $n$ terms $s_n=\frac{2093}{2}$, then $n$ is equal ​to :

    1. (a)$22$
    2. (b)$24$
    3. (c)$23$
    4. (d)$26$
    Show answer

    (c) $23$

    Step-by-step solution →
20. Q200 CBSE 2024
    The sum of the first three terms of an AP is 30 and ​the sum ​of the last three terms is 36. ​If the first ​term is 9, ​then the ​number of ​terms is :

    1. (a)10
    2. (b)5
    3. (c)6
    4. (d)13
    Show answer

    (b) 5

    Step-by-step solution →