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

Question

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

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Answer

The given sequence is $8, 13, 18, 23.....$
Now
$13 - 8 = 5$
$18 - 13 = 5$
$23 - 18 = 5,$ etc
hence the given sequence is an A,P with first term $a = 8$ and common difference $d= 5.$
The general term of an A.P is given by
$t_n=a+(n-1)(5)$
$\Rightarrow402=8+(n-1)(5)$
$\Rightarrow394=5 n-5$
$\Rightarrow399=5 n$
$\Rightarrow n=\frac{399}{5}$
The number of terms cannot be a fraction.
So clearly, $402$ is not the term of the given sequence.

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