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

three consecutive terms in a geometric sequence

Ответ:

jacamron

08.02.2022

Mathematics

9514 1404 393

r = -8

Step-by-step explanation:

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

$\dfrac{r+4}{r}=\dfrac{r+6}{r+4}\\\\1+\dfrac{4}{r}=1+\dfrac{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 $2$}$

_____

Then the terms of the sequence are ...

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

and the common ratio is 1/2.

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Ответ:

jermainedwards

21.05.2022

Mathematics

The ratio of purple flowers total flowers is 9 to 21.

Step-by-step explanation:

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

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