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?

Answer 1

Ok..see!!
so you know the formula for a term in a geometric sequence

an=a×rn−1


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

so in your question you know

2nd term

20=ar2−1...or.....20=ar


and the 4th term

11.25=ar4−1....or....11.25=ar3


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×r2....or........11.25=20×r2


now you just need to solve for r. -----------> and r=0.75 i guess :O
Hope it helps a bit...!

Answer 2

is that 11.25=20 times r squared or 20x times r squared?

Answer 3

20 times r squared.

Answer 4

THANK YOU! :)

Answer 5

yeah np..Anytime :)