Question

$S_n=54+51+48+....n$ terms $=513$. Value of $n$ is

• A. $18$
• B. $19$
• C. $15$
• D. None of these above

Answer 1

Answer: (A), (B)

$18$
$19$

From the given series, we have $S_n=513$

$\Rightarrow \frac{n}{2}\left[2\right(54)+(n-1\left)\right(-3\left)\right]=513$
$\Rightarrow n(108-3n+3)=1026$
$\Rightarrow n^2-37n+342=0$
$\Rightarrow n^2-19n-18n+342=0$
$\Rightarrow n(n-19)-18(n-19)=0$
$\Rightarrow (n-18)(n-19)=0$
Therefore, $n=18$ or $n=19$