Question

$x_1,x_2,x_3,.....$ is an infinite sequence of positive integers in G.P. Such that $x_1{x}_2{x}_3{x}_4=64$. Then the value of $x_5$ is-

• A. Is a perfect square.
• B. Is not a perfect square.
• C. 128
• D. 16

Answer 1

Answer: (A), (D)

16
Is a perfect square.

As all $x_i^{\prime }s$ are positive integers and $x_1,x_2,x_3,x_4=64$
$\Rightarrow x_1,x_2,x_3,x_4$ must be power of 2.
Then, amongst all possible values of $x_1.x_2.x_3.x_4=64$ and in that case $x_5=16$.