Question

What is the value of X in the geometric sequence X, 2, -1/2, ... ?

A. -12
B. -8
C. -4
D. -1/2

Answer 1

B. -8

Explanation:

`\text{If}\ a,\ b,\ c\ \text{is a geometric sequence, then}\ (a)(c)=b^2.\\\\\text{We have}\ x,\ 2,\ -(1)/(2).\ \text{Substitute:}\\\\(x)\left(-(1)/(2)\right)=2^2\\\\-(1)/(2)x=4\qquad\text{multiply both sides by (-2)}\\\\x=-8`