Given that a i > 0 and i belongs to a set of natural numbers. If a 1 , a 2 , a 3 . . . . . a 2 n are in AP, then find the value of a 1 + a 2 n √ a 1 + √ a 2 + a 2 + a 2 n − 1 √ a 2 + √ a 3 . . . . . . . . . . . . + a n + a n + 1 √ a n + √ a n + 1 Options: A . &nbspn-1 B . &nbspna1+a2n√a1+√an+1 C . &nbspn−1√a1+√an+1 D . &nbspn+1√a1+√an+1 E . &nbsp3q+ r

Given that ai > 0 and i belongs to a set of natural numbers. If a1,a2,a3

Question

Given that a_i

>

0 and i belongs to a set of natural numbers. If

a_{1}, a_{2}, a_{3} . . . . . a_{2 n}

are in AP, then find the value of

\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n} - 1}{{\sqrt{a}}_{2} + \sqrt{a_{3}}} . . . . . . . . . . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}}

Answer: Option B
:
B
Let the AP be 1,2,3,4,5
At n=1, the AP = 1,2

a_{1} = 1

and

a_{2} = 2

The value of the expression

= \frac{3}{2.4}

Only option (b) gives this value

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