Question

How many terms of the series $54,51,48,......$ be taken so that their sum is $513$?

• A. $18$
• B. $19$
• C. $20$
• D. $A$ and $B$

Answer 1

The correct option is D $A$ and $B$

Given series is $54,51,48,....$

Sum of $n$ terms of an $A.P.$ is given by:

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$513=\frac{n}{2}[2\times 54+(n-1\left)3\right]$
$1026=n[108-3n+3]$
$1026=111n-3n^2$
$3n^2-111n+1026=0$
$n^2-37n+342=0$
$n^2-18n-19n+342=0$
$n(n-18)-19(n-18)=0$
$(n-18)(n-19)=0$
Then, $n=18$ and $n=19$