Which term of the AP: 3, 8, 13, 18, ……….., is 78 - Vidyadip

Question

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

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Answer

The given AP is $3, 8, 13, 18, .....$
Here $a = 3$
$d = 8 - 3 = 5$
Let the nth term of the $AP$ be $78$.
then, $a_n= a + (n - 1) d$
$ \Rightarrow 78 = 3 + (n - 1) (5) $
$ \Rightarrow 5(n - 1) = 78 - 3$
$ \Rightarrow 5(n - 1) = 75 $
$ \Rightarrow n - 1 = \frac{{75}}{5}$
$ \Rightarrow n - 1 = 15$
$ \Rightarrow n = 15 + 1$
$ \Rightarrow n = 16$

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