Question

. A sum of 1890 is to be used to give seven cash prizes to students of a school for
their overall academic performance. If each prize is 50 less than its preceding prize,
find the value of each of the prizes.​

Answer 1

let first prize be x

so the AP is x,x-50,...........till a7

sn=n/2(2a+(n-1)d

1890=7/2(2x+(7-1)-50

1890=7/2*2x+6*-50

1890=7/2*2x-300

1890*2/7=2x-300

270*2+300=2x

840/2=x

x=420

so,1st prize = 420

2nd =420-50=370

3rd =370-50=320

4th=320-50=270

5th=270-50=220

6th=220-50=170

7th=170-50= 120