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Q : 3 In an AP:

(i) given $\small a=5$ , $\small d=3$ , $\small a_n=50$ , find $\small n$ and $\small S_n$ .

Answers (1)

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It is given that
$a = 5, d = 3 \ and \ a_n = 50$
Let suppose there are n terms in the AP
Now, we know that
$a_n = a+(n-1)d$
$\Rightarrow 50 = 5 + (n-1)3$
$\Rightarrow 48 = 3n$
$\Rightarrow n = 16$
Now, we know that
$S = \frac{n}{2}\left \{ 2a+(n-1)d \right \}$
$\Rightarrow S = \frac{16}{2}\left \{ 2\times(5) +(16-1)(3)\right \}$
$\Rightarrow S = 8\left \{ 10+45\right \}$
$\Rightarrow S = 8\left \{ 55\right \}$
$\Rightarrow S =440$
Therefore, the sum of the given AP is 440

Posted by

Gautam harsolia

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