Question

If the sum of the series $54+51+48+.....$ is $513$, then the number of terms are

• A. $18$
• B. $20$
• C. $17$
• D. None of these

Answer 1

Answer: (A)

$18$

Sum of an AP = $\frac{n}{2}(2a+(n-1)\times d)$ = 513
where $a=54$ and $d=-3$
$\frac{n}{2}(2\times 54+(n-1)\times (-3\left)\right)$ = 513
$\frac{n}{2}(111-3n)$ = 513
$111n-3n^2=1026$
Solving for n,
$n=18$