Question:
Find the sum of 20 terms of the AP $(x+y),(x-y),(x-3 y), \ldots$
Solution:
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
$S=\frac{n}{2}[2 a+(n-1) d]$
Here a = x + y, n = 20, d = - 2y
$\Rightarrow S=10[2 x+2 y+19(-2 y)]=10[2 x+2 y-38 y]=10[2 x-36 y]$
$\Rightarrow S=20[x-18 y]$
Sum of the series is 20(x - 18y).