Is 402 a term of the sequence :

8, 13, 18, 23, ……..?

Since, 13 - 8 = 5, 18 - 13 = 5 and 23 - 18 = 5.

Hence, the series is an A.P. with common difference = 5.

We know that n^th term of an A.P. is given by,

⇒ a_n = a + (n - 1)d, where a is the first term.

Let 402 be n^th term,

⇒ 402 = a + (n - 1)d

⇒ 402 = 8 + (n - 1)5

⇒ 402 = 8 + 5n - 5

⇒ 402 = 5n + 3

⇒ 399 = 5n

⇒ n = $\dfrac{399}{5}$

Since, the no. of term cannot be in fraction.

Hence, 402 is not a term of the sequence.