If (a−b)2,(a2+b2) are the first two terms of an AP, then which of the f

Question -

If $(a - b)^{2}, (a^{2} + b^{2})$ are the first two terms of an AP, then which of the following will be the next term?

Options:

A . 2ab

B .

(a + b)^{2}

C . - 2ab

D .

- (a + b)^{2}

Answer: Option B
:
B
Given,

a_{1} = (a - b)^{2}

a_{1} = a^{2} + b^{2} - 2 a b

and

a_{2} = a^{2} + b^{2}

Now,

d = a_{2} - a_{1}

d = a^{2} + b^{2} - a^{2} - b^{2} + 2 a b

\Rightarrow d = 2 a b

The next term

a_{3} = a_{2} + d

a_{3} = a^{2} + b^{2} + 2 a b = (a + b)^{2}

∴ N e x t t e r m (a_{3}) = (a + b)^{2}

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