Question

If x + 1, 4x + 1, and 8x + 1 are in geometric progression, then what is the non-trivial value of x ?

• A. -1
• B. 1
• C. $\frac{1}{8}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{1}{8}$

Answer 2

If (x + 1) , (4x + 1) and (8x + 1) are in GP. then $(4x + 1)^2 = (x + 1)(8x + 1)$ $\Rightarrow \, 16x^2 + 8x +1 = 8x^2 + x + 8x + 1$ $\Rightarrow\, 8x^2 - x = 0$ $\Rightarrow \, x(8x - 1) = 0$ $\Rightarrow \, x = 0 , \frac{1}{8} , [ \frac{1}{8}$ is non-trivial value]