Q9 of 67 Page 74

A sum of 280 is to be used to give four prizes. If after first prize, each prize is 20 less than the preceding prize, then find the value of each of the prizes.

Given,
Sn = 280, n = 4 and common difference is -20.


Let the first term be a.


Since the sum of n terms is
Sn =


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



So sum of 4 terms S4
]
280 = 2× [2a + 3 × (-20)]
140 = 2a – 60
2a = 140 + 60
2a = 200
a = 100


a1 = a = 100
a2 = a1 + d = 100 - 20 = 80
a3 = a2 + d = 80 - 20 = 60
a4 = a3 + d = 60 - 20 = 40


Hence, The value of prizes are 100, 80, 60 and 40.


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