Question

Find the common ratio for the following geometric sequence? 0.75, 1.5, 3, 6, . . .

3
1.5
2
0.75

Answer 1

`r = 2`

Explanation:

A geometric sequence can be written in the form:
`{a, a*r, a*r^2, a*r^3, ...a*r^(n-1),...}`, where `r` is the common ratio.

`r = 1.5/.75 = 3/1.5 = 6/3 = 2`

Check:
`{ .75, .75*2 = 1.5, .75*2^2 = 3, .75 *2^3 = 6, ...}`

Answer 2

`r=2`

Explanation:

`"the standard geometric sequence is."`

`a, ar, ar^2, ar^3,........, ar^(n-1)`

`"where r is the common ratio"`

`r=(a_2)/(a_1)=(a_3)/(a_2)=...... =(a^n)/(a^(n-1))`

`rArrr=1.5/0.75=3/1.5=2`