A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prices
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Heya!
Given that S= 700. Since each prize is Rs. 20 less than its preceding prize, it means common difference (d) = - 20 and n= 7 ( seven cash prizes )
Putting the values in the formula
Sn= n/2 [ 2a + (n-1) d]
⇒ 700= 7/2 [ 2* a + (7-1) -20]
⇒700= 7/2 [2a + (6) -20]
⇒1400= 7 ( 2a -120)
⇒1400= 14a- 840
⇒2240= 14a
⇒ a= 2240/14 = 160
a= 160. a2= 160-20= 140, a3= 140-20= 120, a4= 120-20= 100 and so on..
So, The value for each price will be Rs. 160, 140, 120, 100, 80, 60 and 40.
Hope it helps
Given that S= 700. Since each prize is Rs. 20 less than its preceding prize, it means common difference (d) = - 20 and n= 7 ( seven cash prizes )
Putting the values in the formula
Sn= n/2 [ 2a + (n-1) d]
⇒ 700= 7/2 [ 2* a + (7-1) -20]
⇒700= 7/2 [2a + (6) -20]
⇒1400= 7 ( 2a -120)
⇒1400= 14a- 840
⇒2240= 14a
⇒ a= 2240/14 = 160
a= 160. a2= 160-20= 140, a3= 140-20= 120, a4= 120-20= 100 and so on..
So, The value for each price will be Rs. 160, 140, 120, 100, 80, 60 and 40.
Hope it helps
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