Question

A sum of 2800 is to be used to award four prizes. If each prize after the first is 200 less than the preceding prize, find the value of each of the prizes.

Answer 1

let the 1st prize be $a_1=a$

and $d=Rs-200$

$a_2=a-200$

$a_3=a-400$

$a_4=a-600$

therefore AP is $a,a-200,a-400,a-600$

$S_4=\frac{4}{2}[2a+[4-1]-200]$

$2800=\frac{4}{2}[2a+3[-200\left]\right]$

$2800\times \frac{2}{4}=2a-600$

$1400=2a-600$

$1400+600=2a$

$2000=2a$

$\frac{2000}{2}=a$

$1000=a$

therefore the first prize is 1000

2nd prize is 1000 -200 =800

3rd prize is 1000-400 =600

4th prize is 1000-600 =400