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

Let the cost of 1^st prize = x

The cost of 2^nd prize $=x-20$

The cost of 3^rd prize $=x-40$

$x,x-20,x-40,\mathrm{.....}$

$a=x,d=-20,n=7$

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

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

$\Rightarrow 1400=7[2x+6(-20)]$

$\Rightarrow 1400=7[2x-120]$

$\Rightarrow 1400=14x-840$

$\Rightarrow 1400+840=14x$

$\Rightarrow 2240=14x\Rightarrow x=\frac{2240}{14}=160$

$\therefore$ The cost of 1^st prize (x) $=160$