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?

Question

campbell_st · Answer

well in a geometric sequence a term can be found by using 

$$a_{n} = ar^{n -1}$$

so you know 

$$20 = ar$$

and you also know 

$$11.25 = ar^3$$

the 4th term can be rewritten as 

$$11.25 = (ar) \times r^2$$

which means its written in terms of the 2nd term 

so 

$$11.25 = 20r^2$$

just solve the equation for r

anonymous · Answer

thanks