CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A

Multiple Choice Questions 

Question. The sum of first five terms of the AP: 3, 7, 11, 15, ... is:
(a) 44
(b) 55
(c) 22
(d) 11
Answer : B

Question. If the first term of an AP is 1 and the common difference is 2, then the sum of first 26 terms is
(a) 484
(b) 576
(c) 676
(d) 625
Answer : C

Question. If the sum to n terms of an AP is 3n2 + 4n, then the common difference of the AP is
(a) 7
(b) 5
(c) 8
(d) 6
Answer : D

Question. If a, b, c are in AP then ab + bc =
(a) b
(b) b2
(c) 2b2
(d) 1/b
Answer : C

Question. The sum of all natural numbers which are less than 100 and divisible by 6 is
(a) 412
(b) 510
(c) 672
(d) 816
Answer : D

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation ofassertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Sum of the first 10 terms of the arithmetic progression –0.5, –1.0, –1.5,... is 27.5.
Reason (R): Sum of first n terms of an AP is given as S_n = n/2 [2a + (n – 1)d] where a = first term, d = common difference.
Answer : A

Question. Assertion (A): The sum of the first n terms of an AP is given by S_n = 3n² – 4n. Then its nth term, a_n = 6n – 7.
Reason (R): nth term of an AP, whose sum of n terms is Sn, is given by a_n = S_n – S_n–1.
Answer : A

Question. Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 500.
Reason (R): Sum of the first n terms of an AP is given by S_n = n/2 [a + l] where l = last term.
Answer : D

Case Study Based Questions

I. Pollution—A Major Problem: One of the major serious problems that the world is facing today is the environmental
pollution. Common types of pollution include light, noise, water and air pollution.

In a school, students thoughts of planting trees in and around the school to reduce noise pollution and air pollution.
Condition I: It was decided that the number of trees that each section of each class will plant 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 a section
of class XII will plant 12 trees.
Condition II: It was decided that the number of trees that each section of each class will plant be the double of the class
in which they are studying, e.g. a section of class I will plant 2 trees, a section of class II will plant 4 trees and so on a
section of class XII will plant 24 trees.

Refer to Condition I

Question. The AP formed by sequence i.e. number of plants by students is
(a) 0, 1, 2, 3, ..., 12
(b) 1, 2, 3, 4, ..., 12
(c) 0, 1, 2, 3, ..., 15
(d) 1, 2, 3, 4, ..., 15
Answer : B

Question. If there are two sections of each class, how many trees will be planted by the students?
(a) 126
(b) 152
(c) 156
(d) 184
Answer : C

Question. If there are three sections of each class, how many trees will be planted by the students?
(a) 234
(b) 260
(c) 310
(d) 326
Answer : A

Refer to Condition II

Question. If there are two sections of each class, how many trees will be planted by the students?
(a) 422
(b) 312
(c) 360
(d) 540
Answer : B

Question. If there are three sections of each class, how many trees will be planted by the students?
(a) 468
(b) 590
(c) 710
(d) 620
Answer : A
 

II. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by paying every month starting with the first instalment of ₹ 1000. If he increases the instalment by ₹ 100 every month, answer the following:

Question. The amount paid by him in 30th installment is
(a) ₹ 3900
(b) ₹ 3500
(c) ₹ 3700
(d) ₹ 3600
Answer : A

Question. The total amount paid by him upto 30 installments is
(a) ₹ 37000
(b) ₹ 73500
(c) ₹ 75300
(d) ₹ 75000
Answer : B

Question. What amount does he still have to pay after 30th installment?
(a) ₹ 45500
(b) ₹ 49000
(c) ₹ 44500
(d) ₹ 54000
Answer : C

Question. If total installments are 40, then amount paid in the last installment is
(a) ₹ 4900
(b) ₹ 3900
(c) ₹ 5900
(d) ₹ 9400
Answer : A

Question. The ratio of the 1st installment to the last installment is
(a) 1 : 49
(b) 10 : 49
(c) 10 : 39
(d) 39 : 10
Answer : B

ARITHMETIC PROGRESSIONS

Please click on below link to download CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A