Answer :
To find : n such that an = a54 + 132
Given: a = 3, d = 15 – 3 = 12
an = 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:
a54 = a + ( 54 - 1)d
= 3 + 53 x 12
= 3 + 636
= 639
Now an = 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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