Question

A sum of ₹700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹20 less than its preceding prize, find the value of each of the prizes.

Answer 1

Here's your answer.......

Answer 2

Answer:

160

Step-by-step explanation:

Considering the AP series - where

Number of the elements = n = 7  (Given)

Sum of all the elements = s = 700 (Given)

Common difference = d = - 20  (Given)

Let the first element be = a

Therefore,

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

s= 7/2 [ 2a + ( 7 - 1 ) (-20) ] .

700 = 7/2 [ 2a + ( 6 × (-20) ) ] .

700 = 7/2 [ 2a - 120 ] .

700 = (7 × 2 )/2 [ a - 60 ] .

7a = 700 + 420 .

7a = 1120 .

a = 160 .

Therefore,  the value of first prize = Rs. 160 .

Since, each term will be 20 less than the previous one, thus the series will be - 160,140,120,100,80....