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Question

Find the sum of the following arithmetic progressions.
(xy)2,(x2+y2),(x+y)2,... to n terms

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Solution

We know,

If a= First term
d= Common difference
n= number of terms

then sum of n term
Sn=n2[2a+(n1)d]

here
a=(xy)2

d=(x2+y2)(xy)2=x2+y2x2y2+2xy

d=2xy

hence

sum Sn=n2[2(xy)2+(n1)2xy]

=n((xy)2+(n1)xy)

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