# A sum of rs700 is to be used to give seven cash prizes to students of a school for their overall academic perfoemance .if each prize us rs20 less than it's preceding price ..find the overall value of each of the prizes ?

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They are in arithmetic progression with a conmon difference of 20

sum of the series is 700

so

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

n=7

d=20

700=(7/2)(2a + 6(20))

simplifiying,

14a =560

a=40..

So the prize amounts are

40 60 80 100 120 140 160.