Question

The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4, or 11.25. What is the common ratio in this sequence?

Answer 1

ok... so you know the formula for a term in a geometric sequence

\[a_{n} = a \times r^{n -1}\]

a is the 1st term and r is the common ratio.

so in your question you know

2nd term

\[20 = ar^{2 -1}...or..... 20 = ar\]

and the 4th term

\[11.25 = ar^{4 -1}....or....11.25 = ar^3\]

the 4th term can be written as ar times r^2 since r * r^2 = r^3

so you can substitute then 2nd term

\[11.25 = ar \times r^2.... or........11.25 = 20 \times r^2\]

now you just need to solve for r.

Answer 2

would r be .75?

Answer 3

@campbell_st

Answer 4

thats right