What is the common difference of an AP in which a₁₈ - a₁₄ = 32
a. 8
b. - 8
c. - 4
d. 4

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Given,

a₁₈ - a₁₄ = 32

a + (18 - 1)d - [a + (14 - 1)d] = 32.

a + 17d - a - 13d = 32.

17d - 13d = 32.

4d = 32

d = 8.

Therefore, d = 8.

✦ Try This: In an AP, the ratio of the 7th term to the 10th term is -1. If the 16th term is -15, what is the 3rd term

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.1 Problem 10

What is the common difference of an AP in which a₁₈ - a₁₄ = 32, a. 8, b. - 8, c. - 4, d. 4

Summary:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. The common difference of an AP in which a₁₈ - a₁₄ = 32 is 8

☛ Related Questions:

• Two APs have the same common difference. The first term of one of these is -1 and that of the other . . . .
• If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be, a. . . . .
• The 4th term from the end of the AP: -11, -8, -5, ...,49 is, a. 37, b. 40, c. 43, d. 58