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State True/False.

184 is a term of the $AP 3, 7, 11, 15, …$

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False

True

answer is B.

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Detailed Solution

Given A.P. is

3, 7, 11, 15, … …

So, first term:

t 1 = 3

, second term:

t 2 = 7

∴ d = t 2 − t 1 ⇒ d = 7 − 3 = 4

Formula used for nth term of A.P.:

t n = a + n − 1 d

Let 184 is nth term of AP and apply formula of nth term of AP:

∴ t n = a + (n − 1) d ⇒ 184 = 3 + (n − 1) × 4 ⇒ 184 − 3 = 4 n − 4 ⇒ 181 = 4 n − 4

⇒ 4 n = 181 + 4 ⇒ n = 1854 ⇒ n = 4614

As the number of terms cannot be a fraction, therefore 184 is not a term of A.P.
Thus, the given statement is false.
Hence, option (2) is correct.

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