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nth Term of an AP

If T n =78, w...

Question

If $T_{n} = 78$ , where $T_{n}$ denotes the $n^{t h}$ term the following AP:
3, 8, 13, 18, . . . , then n = ___

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Solution

Here, first term, $a = 3$

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.}
$\Rightarrow 78 = 3 + (n - 1) 5$
$\Rightarrow 75 = 5 n - 5$
$\Rightarrow 80 = 5 n$
$\Rightarrow n = \frac{80}{5} = 16$
It means $16^{t h}$ term of the given AP is equal to 78.

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