Question

How do you find the common ratio, r, for the geometric sequence that has a1 =100 and a8 =50?

Answer 1

`r = (1/2)^(1/7)~~0.9057`

Explanation:

The key to solving this problem is in recognizing what the terms of a geometric sequence look like. If we write a geometric sequence in its most general form, we have:

`a_1 = a_1`
`a_2 = a_1r`
`a_3 = a_1r^2`
...
`a_n = a_1r^(n-1)`

In this case `a_8 = 50`. But, using `a_1 = 100`, we have

`50 = a_8 = a_1r^(8-1) = 100r^7`

`=>r^7 = 50/100 = 1/2`

`:.r = (1/2)^(1/7)~~0.9057`