Question

What is the common ratio of the sequence `-164, -82, -41, -20.5...`?

Answer 1

Common ratio: `1/2`

Explanation:

If `r` is the common ratio
`color(white)("XXX")(-164)xxr=-82`
`color(white)("XXXXXXXXXXXXX")rarr r= (-82)/(-164) = 1/2`

We could verify this result by checking that for `r=1/2`
`color(white)("XXX")(-82)xx r = -41`
and
`color(white)("XXX")(-41)xxr = -20.5`
(which, fortunately, they do).

Answer 2

`r = (-82)/(-164) = 1/2`

Explanation:

To find the common ratio in a GP, divide a term by the term preceding it. Test that this gives the same answer for any two consecutive terms.

`r = T_3/T_2 = T_5/T_4 = T_n/T_(n-1)`

`r = (-82)/(-164) = 1/2`

`r = (-41)/(-82) = 1/2` etc