Class 10 Maths · Chapter 5

Arithmetic Progressions

137 Class 10 Maths questions on Arithmetic Progressions from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

NCERT exercises

Exercise 5.1 (4) Exercise 5.2 (20) Exercise 5.3 (20) Exercise 5.4 (0)

NCERT Exemplar exercises

Exercise 5.1 (18) Exercise 5.2 (7) Exercise 5.3 (35) Exercise 5.4 (0)

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 3 of 7

Q41 NCERT · Exercise 5.3

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

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The students will plant a total of $234$ trees.

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Q42 NCERT · Exercise 5.3

A spiral is made up of successive semicircles, with centres alternately at $A$ and $B$ , starting with centre at $A$ , of radii $0.5$ cm, $1.0$ cm, $1.5$ cm, $2.0$ cm, $\dots$ as shown in Fig. $5.4$ . What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $π = \frac{22}{7}$ .)
Fig. 5.4

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The total length of the spiral is $143$ cm.

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Q43 NCERT · Exercise 5.3

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Fig. 5.5). In how many rows are the 200 logs placed and how many logs are in the top row?
Fig. 5.5

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The $200$ logs are placed in $16$ rows, and the top row contains $5$ logs (the root $n = 25$ is rejected because it would make the top row hold $- 4$ logs).

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Q44 NCERT · Exercise 5.3

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Fig. 5.6). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? [Hint: To pick up the first potato and the second potato, the total distance (in metres) run by a competitor is $2 \times 5 + 2 \times (5 + 3)$ .]
Fig. 5.6

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The competitor runs a total distance of $370$ m.

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Q45 Exemplar · Exercise 5.1
In an AP, if $d = - 4$ , $n = 7$ , $a_{n} = 4$ , then $a$ is
1. (a) $6$
2. (b) $7$
3. (c) $20$
4. (d) $28$
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(d) $28$

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Q46 Exemplar · Exercise 5.1
In an AP, if $a = 3.5$ , $d = 0$ , $n = 101$ , then $a_{n}$ will be
1. (a) $0$
2. (b) $3.5$
3. (c) $103.5$
4. (d) $104.5$
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(b) $3.5$

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Q47 Exemplar · Exercise 5.1
The list of numbers $- 10, - 6, - 2, 2, \dots$ is
1. (a)an AP with $d = - 16$
2. (b)an AP with $d = 4$
3. (c)an AP with $d = - 4$
4. (d)not an AP
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(b) an AP with $d = 4$

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Q48 Exemplar · Exercise 5.1
The 11th term of the AP: $- 5, - \frac{5}{2}, 0, \frac{5}{2}, \dots$ is
1. (a) $- 20$
2. (b) $20$
3. (c) $- 30$
4. (d) $30$
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(b) $20$

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Q49 Exemplar · Exercise 5.1
The first four terms of an AP, whose first term is $- 2$ and the common difference is $- 2$ , are
1. (a) $- 2, 0, 2, 4$
2. (b) $- 2, 4, - 8, 16$
3. (c) $- 2, - 4, - 6, - 8$
4. (d) $- 2, - 4, - 8, - 16$
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(c) $- 2, - 4, - 6, - 8$

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Q50 Exemplar · Exercise 5.1
The $2 1^{s t}$ term of the AP whose first two terms are $- 3$ and $4$ is
1. (a)17
2. (b)137
3. (c)143
4. (d)-143
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(b) 137

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Q51 Exemplar · Exercise 5.1
If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
1. (a)30
2. (b)33
3. (c)37
4. (d)38
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(b) 33

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Q52 Exemplar · Exercise 5.1
Which term of the AP: 21, 42, 63, 84, ... is 210?
1. (a)9th
2. (b)10th
3. (c)11th
4. (d)12th
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(b) 10th

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Q53 Exemplar · Exercise 5.1
If the common difference of an AP is $5$ , then what is $a_{18} - a_{13}$ ?
1. (a)5
2. (b)20
3. (c)25
4. (d)30
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(c) 25

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Q54 Exemplar · Exercise 5.1
What is the common difference of an AP in which $a_{18} - a_{14} = 32$ ?
1. (a) $8$
2. (b) $- 8$
3. (c) $- 4$
4. (d) $4$
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(a) $8$

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Q55 Exemplar · Exercise 5.1
Two APs have the same common difference. The first term of one of these is $- 1$ and that of the other is $- 8$ . Then the difference between their 4th terms is
1. (a) $- 1$
2. (b) $- 8$
3. (c) $7$
4. (d) $- 9$
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(c) $7$

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Q56 Exemplar · Exercise 5.1
If 7 times the $7^{th}$ term of an AP is equal to 11 times its $1 1^{th}$ term, then its 18th term will be
1. (a) $7$
2. (b) $11$
3. (c) $18$
4. (d) $0$
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(d) $0$

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Q57 Exemplar · Exercise 5.1
The 4th term from the end of the AP: $- 11, - 8, - 5, \dots, 49$ is
1. (a) $37$
2. (b) $40$
3. (c) $43$
4. (d) $58$
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(b) $40$

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Q58 Exemplar · Exercise 5.1
The famous mathematician associated with finding the sum of the first 100 natural numbers is
1. (a)Pythagoras
2. (b)Newton
3. (c)Gauss
4. (d)Euclid
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(c) Gauss

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Q59 Exemplar · Exercise 5.1
If the first term of an AP is $- 5$ and the common difference is $2$ , then the sum of the first $6$ terms is
1. (a) $0$
2. (b) $5$
3. (c) $6$
4. (d) $15$
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(a) $0$

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Q60 Exemplar · Exercise 5.1
The sum of first 16 terms of the AP: $10, 6, 2, \dots$ is
1. (a) $- 320$
2. (b) $320$
3. (c) $- 352$
4. (d) $- 400$
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(a) $- 320$

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