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 this sequence?

Can you show me the steps to how this is solved thank you!

Answer 1

\[r=\frac{ a _{n+1} }{ a _{n} }\]\[r=\frac{ a _{3} }{ 50 }\]\[r=\frac{ 112.5 }{ a _{3} }\]Since r is common to both ratios, set them equal to each other.\[\frac{ 112.5 }{ a _{3} }=\frac{ a _{3} }{ 50 } \]
Once you find what a sub 3 is, you can substitute into one the ratios and solve for r.