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in Arithmetic Progression by (50.9k points)
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Find the sum of 20 terms of the AP (x + y), (x – y), (x – 3y), ….

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To Find: The sum of 20 terms of the given AP.

Sum of n terms of an AP with first term a and common difference d is given by

s = n/2[2a+(n -1)d]

Here a = x + y, n = 20, d = - 2y

⇒ S = 10[2x + 2y + 19( - 2y)] = 10[2x + 2y - 38y] = 10[2x - 36y]

⇒ S = 20[x - 18y]

Sum of the series is 20(x - 18y).

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