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

Solution:

The formula for n^th term of an arithmetic progression is aₙ = a + (n - 1) d .

Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.

Given AP is 3, 15, 27, 39.

First term a = 3

Second term a + d = 15

d = 15 - 3 = 12

54^th term of the AP is

a₅₄ = a + (54 - 1)d

= 3 + 53 × 12

= 3 + 636

= 639

Let n^th term of AP be 132 more than 54^th term

We get, 132 + 639 = 771

aₙ= 771

aₙ = a + (n - 1)d

771 = 3 + (n - 1)12

768 = (n - 1)12

(n - 1) = 64

n = 65

Therefore, the 65^th term will be 132 more than the 54^th term.

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

Video Solution:

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

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 11

Summary:

The 65^th term of the AP 3,15, 27, 39 will be 132 more than its 54^th term.

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