Question

Which term of the AP : 3, 8, 13, 18, . . . . is 78?

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Answer 1

Given a=3

Common difference, $d=8-3=13-8=5$
$a_n=78$
Using formula $a_n=a+(n-1)d$ to find nth term of arithmetic progression, we get
$a_n=3+(n-1)5$ {we want to find value of n here.}
$\Rightarrow 78=3+(n-1)5$
$\Rightarrow 75=5n-5$
$\Rightarrow 80=5n$
$\Rightarrow n=\frac{80}{5}=16$
It means ${16}^{th}$ term of the given AP is equal to 78.