Is 302 a term of the A.P. 3, 8, 13,…?
Given A.P is 3, 8, 13,…
Here, a1 = a = 3, a2 = 8
Common difference, d = a2 – a1 = 8 – 3 = 5
We know, an = a + (n – 1)d where a is first term or a1 and d is common difference and n is any natural number
∴ an = 3 + (n – 1)5
⇒ an = 3 + 5n – 5
⇒ an = 5n – 2
To find: whether 302 is a term of this A.P. or not
Put an = 302
∴ 5n – 2 = 302
⇒ 5n = 302 + 2
⇒ 5n = 304
is not a natural number
Hence,304 is not a term of given A.P.