Answered

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

Sagot :

Answer:

x ≈ 0.17

Step-by-step explanation:

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

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] , substitute values

[tex]\frac{2x+1}{x}[/tex] = [tex]\frac{4x+10}{2x+1}[/tex] ( 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 = [tex]\frac{1}{6}[/tex] ≈ 0.17 ( to the nearest hundredth )

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