Answer :

Given A.P is 3, 8, 13,…

Here, a_{1} = a = 3, a_{2} = 8

Common difference, d = a_{2} – a_{1} = 8 – 3 = 5

We know, a_{n} = a + (n – 1)d where a is first term or a_{1} and d is common difference and n is any natural number

∴ a_{n} = 3 + (n – 1)5

⇒ a_{n} = 3 + 5n – 5

⇒ a_{n} = 5n – 2

To find: whether 302 is a term of this A.P. or not

Put a_{n} = 302

∴ 5n – 2 = 302

⇒ 5n = 302 + 2

⇒ 5n = 304

is not a natural number

Hence,304 is not a term of given A.P.

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