If $T_{n} = 78$ , where $T_{n}$ denotes the $n^{t h}$ term the following A.P.:
$3, 8, 13, 18$ , . . . , then find the value of $n$ .
[3 Marks]

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Solution

Here, first term, $a = 3$

Common difference, $d = 8 - 3 = 13 - 8 = 5$
[0.5 Marks]

$a_{n} = 78$
To find nth term of arithmetic progression,
$a_{n} = a + (n - 1) d$
[1 Mark]

$78 = 3 + (n - 1) 5$
$\Rightarrow 78 = 3 + (n - 1) 5$
$\Rightarrow \frac{75}{5} = n - 1$
$\Rightarrow 15 = n - 1$
$\Rightarrow n = 16$
It means $16^{t h}$ term of the given A.P. is equal to 78.
[1.5 Marks]

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