# 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.

As, each price is decreased by 20 rupees, we can consider amount given to each student in increasing order to be an AP.
Let the lowest price given be 'a' and then prize is increased by Rs 20.
In that case, we have
First term = a
Common difference, d = - 20
No of terms, n = No of students getting prize = 7
Sum of 'n' terms = Total prize money = 700

Now,

we know, sum of 'n' terms on AP is ⇒ 700 × 2 = 7[2a - 120]
⇒ 200 = 2a - 120
⇒ 2a = 200 + 120
⇒ 2a = 320
⇒ a = 160
Hence, the divisions are Rs. 160, Rs. 140, Rs. 120, Rs. 100, Rs. 80, Rs. 60, Rs. 40

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