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

consider the series as an AP series
where
first element = a
common difference(d)=-20
no of elements(n) =7
sum of all elements(s)= 700
s=n/2 (2a+(n-1)d)
700=7/2 (2a+(7-1)(-20))
200=2a-120
320=2a
a=160
hence the series will be
160,140,120,100,80,60,40

Answer 2

"The series

160,140,120,100,80,60,40

Given:

Rs. 700 for seven cash prizes

To find:

The series

Solution:

Consider the series as an AP series

where

First element = a

Common difference(d) = - 20

Number of elements(n)  = 7

Sum of all elements(s) = 700

$s = \frac{n}{2}(2 a + (n - 1) d)$

$700 = \frac{7}{2}(2 a + (7 - 1)( - 20))$

200 = 2 a - 120

320 = 2a

a = 160

Each term will be 20 less than the previous one.

Hence the series will be

160,140,120,100,80,60,40."