In an A.P. if $a = 12$ , $d = 4$ , $T_{n} = 76$ , find $n$

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Solution

We know that the formula for the nth term is $t_{n} = a + (n - 1) d$ , where $a$ is the first term, $d$ is the common difference.

It is given that the first term is $a = 12$ , the nth term is $t_{n} = 76$ and the difference is $d = 4$ , therefore,

$t_{n} = a + (n - 1) d \Rightarrow 76 = 12 + (n - 1) 4 \Rightarrow 76 = 12 + 4 n - 4 \Rightarrow 76 = 4 n + 8 \Rightarrow 4 n = 76 - 8 \Rightarrow 4 n = 68 \Rightarrow n = \frac{68}{4} = 17$

Hence, $n = 17$

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