Question

*
24. Find the sum of:
x2 - y2 y2 - 22 and 22 – x2 is

Answer 1

Answer:

We have to find the sum of (x−y)

2

,(x

2

+y

2

),(x+y)

2

,... to n terms

From the progression we know that first term is a=(x−y)

2

Now, let's calculate the common difference d

d=a

2

−a

1

=(x

2

+y

2

)−(x−y)

2

=(x

2

+y

2

)−(x

2

+y

2

−2xy)

=x

2

+y

2

−x

2

−y

2

+2xy

=2xy

We know that the sum of an A.P is given by S

n

=

2

n

×{2a+(n−1)d}

So,

S

n

=

2

n

×{2(x−y)

2

+(n−1)×2xy}

=

2

n

×2{(x−y)

2

+(n−1)xy}

=n{(x−y)

2

+(n−1)xy}