Answer :

**To find : n such that a _{n} = a_{54} + 132**

Given: a = 3, d = 15 – 3 = 12

a

_{n}= a + (n - 1) d

where,

a = first term of AP

n = no. of terms of AP

d = common difference of AP

54th term can be given as follows:

a_{54} = a + ( 54 - 1)d

= 3 + 53 x 12

= 3 + 636

= 639

Now a

_{n}= 771, n = ?

Again applying the formula of nth term

771 = a + (n – 1)d

771 = 3 + (n -1)12

(n – 1)12 = 771 – 3 = 768

n - 1 = 768/12

n – 1 = 64

n = 65

**Thus, the required term is 65th term.**

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