Question

If a geometric sequence has a2 = 495 and a6 = 311, approximate the value of the common ratio ???? to four decimal

places.

Answer 1

`r = 0.8903`

Explanation:

given,

a₂ = 495

a₆ = 311

geometric sequence formula

`a_n = ar^(n-1)`

`a_2 = ar^(2-1)`

`a_2 = ar`...................(1)

`a_6 = ar^(6-1)`

`a_6 = ar^5`................(2)

dividing equation (2) by (1)

`(a_6)/(a_2) = (ar^5)/(ar)`

`(311)/(495) = r^4`

`r^4 = 0.628`

`r = 0.8903`

hence, the common ratio of the geometric sequence is
`r = 0.8903`