For x 0 , the least value of a , for which 5 1 + x + 5 1 - x , a 2 , 25 x + 25 - x are three consecutive terms of an A.P., is equal to:

Question

For $x \geq 0$ , the least value of $a$ , for which $5^{1 + x} + 5^{1 - x}, \frac{a}{2}, 25^{x} + 25^{- x}$ are three consecutive terms of an A.P., is equal to:

Smart Achievers · Accepted Answer

(2)

$Let 5^{x} = t; t > 0$

$A . M . \geq G . M .$

$y^{2} + 5 y - (2 + a) = 0;$ $where y = t + \frac{1}{t} \geq 2$

$Since a \geq 12$

Solution

Q.
For $x \geq 0$ , the least value of $a$ , for which $5^{1 + x} + 5^{1 - x}, \frac{a}{2}, 25^{x} + 25^{- x}$ are three consecutive terms of an A.P., is equal to:

1 8

2 12

3 10

4 16

Ans.
(2)

$Let 5^{x} = t; t > 0$

$A . M . \geq G . M .$

$y^{2} + 5 y - (2 + a) = 0;$ $where y = t + \frac{1}{t} \geq 2$

$Since a \geq 12$

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