Which term of the A.P. 4, 9, 14, ... is 89?

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answer is D.

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Detailed Solution

Given A.P. is 4, 9, 14, …,89,…..
The formula to calculate the

n^{th}

term in A.P. is given by,

a n = a + n − 1 d

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

d = a 2 − a 1 ⇒ d = 9 − 4 ⇒ d = 5

Therefore, according to the question,

89 = 4 + n − 1 5 ⇒ 5 n − 1 = 89 − 4 ⇒ n − 1 = 17 ⇒ n = 18

So, 89 is the

1 8^{th}

term in the given A.P.
Hence, option 4 is correct.

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