Find the $n^{t h}$ term and, hence, the $25^{t h}$ term of the following AP: $2, 5, 8, 11$ ,.........

3 n - 1, 74

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2 n, 73

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3 n, 75

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3 n + 1, 72

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Solution

The correct option is A $3 n - 1, 74$
Given series, 2, 5, 8, 11, ... is in AP
Here
First term $a = 2$
Common difference $d = 5 - 2$
$= 8 - 5$
$= 3$
We know that, general term
$t_{n} = a + (n - 1) d$
$= 2 + (n - 1) 3$
$= 2 + 3 n - 3$
$= 3 n - 1$
$t_{25} = 3 \times 25 - 1$
$= 75 - 1 = 74$

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