Question

Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54^th term?

Options

• 70

• 65

• 80

• 55

Answer 1

65

Explanation:-

Let’s first calculate 54^th of the given AP.

First term = a = 3

Common difference = d = 15 - 3 = 12

Using formula a_n=a + (n - 1)d, to find n^th term of arithmetic progression, we get

a₅₄ = a + (54 - 1)d

a₅₄ = 3 + 53(12) = 3 + 636 = 639

We want to find which term is 132 more than its 54^th term.

Let’s suppose it is n^th term which is 132 more than 54^th term.

Therefore, we can say that

a_n = a₅₄ + 132

a_n = a + (n - 1)d = 3 + (n - 1)(12)

⇒ 3 + (n - 1)12 = 639 + 132

⇒ 3 + 12n - 12 = 771

⇒ 12n - 9 = 771

⇒ 12n = 780

⇒ n = `780/12` = 65

Therefore, 65^th term is 132 more than its 54^th term.