Question

three consecutive terms in a geometric sequence are r ,r+4, and r+6 in that order. Determine the value of r.​

Answer 1

Answer: r = -8

Explanation:

Answer 2

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Answer:

r = -8

Explanation:

The terms of a geometric sequence have a common ratio, so we have ...

`(r+4)/(r)=(r+6)/(r+4)\\\\1+(4)/(r)=1+(2)/(r+4)\\\\4(r+4)=2(r)\qquad\text{subtract 1, cross multiply}\\\\2r=-16\qquad\text{subtract $2r+16$}\\\\\boxed{r=-8}\qquad\text{divide by $2$}`

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Then the terms of the sequence are ...

-8, -4, -2, ...

and the common ratio is 1/2.