In an AP if $a = 1$ , $a_{n} = 20$ and $S_{n} = 399$ , then $n$ is

19

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21

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38

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42

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Solution

The correct option is B $38$
$a = 1$
$a_{n} = 20$
$S_{n} = 399$
Then,
$\Rightarrow a_{n} = a + (n - 1) d$
$\Rightarrow 20 = 1 + (n - 1) d$
$\Rightarrow 19 = (n - 1) d$
Also given,
$S_{n} = \frac{n}{2} \times$ $[2 a + (n - 1) d]$
Substituting values,
$399 \times 2 = n (2 + 19)$
$\Rightarrow 798$ = $n \times 21$
$n = 38$

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