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Which term of the A.P. 3, 15, 27, 39, ... will be 132 more than its $5 4^{th}$ term?

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answer is D.

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Detailed Solution

Given A.P. is A.P. 3, 15, 27, 39, ...
We know the formula,

a n = a + n − 1 d

Where,
The first term is a.
The common difference is d.
The number of terms are n.
According to the question,
The common difference will be,

d = a 2 − a 1 ⇒ d = 15 − 3 ⇒ d = 12

Now,

a 54 = a 1 + 54 − 1 d ⇒ a 54 = 3 + 5312 ⇒ a 54 = 639

Also,

a n = a 54 + 132 ⇒ a n = 639 + 132 ⇒ a n = 771

Again,

771 = 3 + n − 1 12 ⇒ 771 − 3 12 = n − 1 ⇒ 64 + 1 = n ⇒ n = 65

So, the term that is 132 more than the

54^{th}

term is the

65^{th}

term.
Hence, option 4 is correct.

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