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in Arithmetic Progression by (36.5k points)
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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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Total/Sum of all cash prizes = Rs. 700 

Each prize differs by Rs. 20 

Let the prizes (in ascending order) be x, x + 20, x + 40, x + 60, x + 80, x + 100, x + 120 

∴ Sum of the prizes = S7 = \(\frac{n}{2}\)(a + l) 

⇒ 700 = \(\frac{7}{2}\) [x + x + 120] 

⇒ 700 × \(\frac{7}{2}\) = 2x + 120 

⇒ 100 = x + 60 

⇒ x = 100 – 60 = 40 

∴ The prizes are 160, 140, 120, 100, 80, 60, 40.

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