Chapter 5 Arithmetic Progressions Assertation & Reasoning Questions Class 10th

Direction: 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 of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1.) Assertion: Sum of natural number from 1 to 100 is 5050

 reason: Sum of n natural number is n(n+1)/2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

2.) Assertion: Sum of fist n terms in an A.P. is given by the formula: Sn = 2n×[2a+(n−1)d]

reason: Sum of first 15 terms of 2+5+8——- is 345.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

4.) Assertion: The constant difference between any two terms of an AP is commonly known as common difference

Reason: the common difference of 2,4,6,8 this A.P. sequence is 2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

5.) Assertion: Arithmetic progression is a sequence of numbers in which the difference of any two adjacent terms is constant.

Reason :4,8,12,16 this sequence is an A.P.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

6.) Assertion: If numbers a,b,c are in A.P then b-a=c-b

reason: given three numbers are in AP, then the common difference will be same.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

7.) Assertion: The sum of series with the nth term tn= (9-5n) is 220 when no. of terms n=6

reason : Sum of first n terms in an A.P. is given by the formula: Sn = 2n×[2a+(n−1)d]

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

 8.)Assertion: An AP containing a finite number of terms is called finite AP

Reason: 3,5,7,9,11,13,15,17,19,21 is an finite AP

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

9.)Assertion: the value of n, if a = 10, d = 5, an = 95.

Reason: the  formula of general term an is an= a+(n-1)d.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

10.) Assertion: arithmatic between 5 and 90 is 47.5

Reason: arithmatic between two given number a,b is (a+b)/2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

11.) Assertion: The 11 th term of an AP is 7,9,11,13_________is 67

Reason: if sn is the sum of first n terms of an AP then its nth term an is given by an=sn+sn-1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are false.

12.Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.

Answer: (a)

13.Assertion : If S_n is the sum of the first n terms of an A.P., then its nth term an is given by a_n = S_n – S_{n – 1} .
Reason : The 10th term of the A.P. 5, 8, 11, 14, ………………. is 35.

Answer: (c)

14. Assertion : The sum of the series with the nth term, t_n = (9 – 5n) is (465), when no. of terms n = 15.
Reason : Given series is in A.P. and sum of n terms of an A.P. is

Answer: (d)