Question

If $S=1\left(25\right)+2\left(24\right)+3\left(23\right)+......+24\left(2\right)+25\left(1\right)$ , then the value of $\frac{S}{900}$ is equal to

Answer 1

Answer: 3.25

$S={\sum }_{r=1}^{25}r(26-r)=26{\sum }_{r=1}^{25}r-{\sum }_{r=1}^{25}{r}^2$
$=26\times \frac{25\times 26}{2}-\frac{25\times 26\times 51}{6}$
$=\frac{25\times 26}{2}\left(26-\frac{51}{3}\right)=\frac{25\times 2613}{4}\times 9$
$\Rightarrow \frac{S}{900}=\frac{13}{4}=3.25$