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Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?

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answer is D.

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Detailed Solution

Given A.P. is. 3, 10, 17, 24,..
We know,
The

n^{th}

of an arithmetic progression is

a n = a + n − 1 d

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

a 13 = 3 + 13 − 1 7 ⇒ a 13 = 3 + 12 × 7 ⇒ a 13 = 3 + 84 ⇒ a 13 = 87

Therefore, the term which is 84 more than the

13 t h

the term is 87+84=171.
Now substituting 171 in

n^{th}

term formula,

171 = 3 + n − 1 7 ⇒ 171 − 3 7 = n − 1 ⇒ 24 = n − 1 ⇒ n = 25

So, the

25 t h

term of the A.P is 84 more than the

13 t h

term.
Therefore, option 4 is correct.

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