Question

For the geometric sequence x, (2x + 1), (4x + 10), ... the value of x, to the nearest

Answer 1

Answer:

x ≈ 0.17

Step-by-step explanation:

There is a common ratio r between consecutive terms in a geometric sequence, that is

r = $\frac{a_{2} }{a_{1} }$ = $\frac{a_{3} }{a_{2} }$ , substitute values

$\frac{2x+1}{x}$ = $\frac{4x+10}{2x+1}$ ( cross- multiply )

x(4x + 10) = (2x + 1)² ← expand using FOIL

4x² + 10x = 4x² + 4x + 1 ( subtract 4x² + 4x from both sides )

6x = 1 ( divide both sides by 6 )

x = $\frac{1}{6}$ ≈ 0.17 ( to the nearest hundredth )