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Arithmetic Progressions
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02/06/2021 10:44 am
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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 of the prizes.
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02/06/2021 10:47 am
Let the cost of 1st prize be Rs. P.
Cost of 2nd prize = Rs. P − 20
And cost of 3rd prize = Rs. P − 40
common difference as −20 and first term as P.
Thus, a = P and d = −20
Given that, S7 = 700
Sn = n/2 [2a + (n – 1)d]
= 7/2 [2a + (7 – 1)d] = 700
= \(\frac{[2a + (6)(-20)]}{2} = 20\)
a + 3(−20) = 100
a −60 = 100
a = 160
Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.