Question

If $x\in R$, the numbers $\left(5^{1+x}+5^{1-x}\right),a/2,\left(25^x+25^{-x}\right)$ form an A.P. then ' $a$ ' must lie in the interval

• A. $[1,5]$
• B. $[2,5]$
• C. $[5,12]$
• D. $[12,\infty )$

Answer 1

Answer: (D)

$5^{1+x}+5^{1-x},a/2,25^x+25^{-x}$
$2\left(\frac{a}{2}\right)=5\left(5^x+\frac{1}{5^x}\right)+\left(25^x+\frac{1}{25^x}\right)$
$a_{\min }=5(2)+2=12$
$a_{\max }=\infty \Rightarrow [12,\infty )$