Question

the second term in a geometric sequence is 50. the fourth term in the same sequence is 112.5. what is the common ratio in the sequence?

Answer 1

\[a_1,r \cdot a_1, r^2 a_1 ,r^3 \cdot a_1 , r^4 \cdot a_1, \cdots ,a_1 \cdot r^{n-1}, \cdots \\ \text{ where the } n^{ \text{ th }} \text{ term is given by } a_n=a_1 \cdot r^{n-1}\]

you want to solve for r.

Answer 2

\[\frac{ a_4}{a_2}= \frac{a_1 \cdot r^{3}}{a_1 \cdot r}=\frac{r^3}{r} \text{ continue to simplify this and use what you are given by this ratio }\]

Answer 3

got cut off
suppose to say
use what you are given by the ratio to solve for r