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

9514 1404 393

Answer:

  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.

Answer 2

Answer: r = -8

Step-by-step explanation: