# Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54th term? - Mathematics

Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54thterm?

#### Solution

Given A.P. is 3, 15, 27, 39, …

= 3

d = a2 − a1 = 15 − 3 = 12

a54 = a + (54 − 1) d

= 3 + (53) (12)

= 3 + 636 = 639

132 + 639 = 771

We have to find the term of this A.P. which is 771.

Let nth term be 771.

an = a + (n − 1) d

771 = 3 + (n − 1) 12

768 = (n − 1) 12

(n − 1) = 64

n = 65

Therefore, 65th term was 132 more than 54th term.

Alternatively,

Let nth term be 132 more than 54th term.

n = 54 + 132/12

= 54 + 11 = 65th term

Concept: nth Term of an AP
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.2 | Q 11 | Page 106