Question

A sum of Rs. $700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. $20$ less than its preceding prize, find the value of each prize.

Answer 1

Let the value of the prices be

$x,x-20,x-40$, .....

This is an arithmetic sequence with first term $\left(a\right)=x$, $n=7$ and common difference $\left(d\right)=-20.$

Given,

$S_n$ = 700

$\Rightarrow \frac{n}{2}[2a+(n-1\left)d\right]=700$

$\Rightarrow \frac{7}{2}\left[2\right(x)+(7-1\left)\right(-20\left)\right]=700$

$\Rightarrow 2x-120=700\times \frac{2}{7}$

$\Rightarrow 2x=200+120$

$\Rightarrow x=\frac{320}{2}=160$

Thus, the values of the prizes are Rs. $160,Rs.140,Rs.120,Rs.100,$ $Rs.80,Rs,60$ and $Rs.40$.