Question

Find the sum of following AP
(2) (x - y)2, (x2 + y2), (x + y)2, ... up to n terms​

Answer 1

(x – y)2 , (x2, y2), (x + y)2, . . . to n terms.

Common difference of the A.P. (d) = a2 – a1

= (x2 – y2) – (x – y)2

= x2 + y2 – (x2 + y2 – 2xy)

= 2xy

Number of terms (n) = n

First term for the given A.P. (a) = (x – y)2

We know that,

Sum of n terms of an A.P.= Sn=n2[2a+(n–1)d]

Then, according to the question,

Sn=n2[2(x–y)2+(n–1)2xy]

= n2(2)[(x–y)2+(n–1)xy]

= (n)[ ( x – y )2 + ( n – 1 )xy ]

∴, the sum of first n terms of the given A.P. is (n)[ ( x – y )2 + ( n – 1 )xy ]

 

Answer 2

Step-by-step explanation:

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