Is $402$ a term of the sequence:
$8, 13, 18, 23, . . . . . . . . . . . . . . . . . . ?$

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Solution

$8, 13, 18, 23, . . . . . . . . . . . . . .$

$a = 8, d = 5$

$T_{n} = a + (n - 1) d$

$402 = 8 + (n - 1) 5$

$402 = 8 + 5 n - 5$

$402 = 3 + 5 n$

$5 n = 399$

$n = \frac{399}{5}$

The number of the series cannot be a fraction. So, 402 is not a term of given series.

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