Question

four students wrote sequences in math class. angela -6,-9,-12,-15,... bradley -2,-6, -12,-24,... carter -1, -3, -9, -27,... dominique -1, -3,-9, -81,... which student wrote a geometric sequence? a)angela b)bradley c)carter d)dominique

Answer 1

carter

Explanation:

edg 2020 december 10th

Answer 2

c) carter

Explanation

Remember that A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a fixed number called the ratio. So to prove if a sequence is geometric, y we just need to verify that the ratio between any tow terms of the sequence is the same.

Now, to find the ratio of a geometric sequence, we use the formula:

`r=(a_(n))/(a_(n-1))`

`r` is the ratio

`a_(n)` is the current term

`a_(n-1)` is the previous term

The formula just mean that we can find the ratio by dividing the current term and the previous term.

Let's apply this to our sequences:

Angela -6,-9,-12,-15,...

Take -9 as the current term and -6 as the previous term, so
`a_(n)=-9` and
`a_(n-1)=-6`; now let's find the ratio.

`r=(a_(n))/(a_(n-1))`

`r=(-9)/(-6) =(3)/(2)`

Lets check if the ratio hold for the next pair -9 and -12.
`a_(n)=-12` and
`a_(n-1)=-9`, so

`r=(-12)/(-9) =(4)/(3)`

The ratio is not the same, so Angela's sequence is not a geometric one.

Bradley -2,-6, -12,-24,...

For -2 and -6

`r=(a_(n))/(a_(n-1))`

`r=(-6)/(-2) =3`

For -6 and -12

`r=(-12)/(-6) =2`

The ratio is not the same, so Bradley's sequence is not a geometric one.

Carter -1, -3, -9, -27,...

For -1 and -3

`r=(-3)/(-1) =3`

For -3 and -9

`r=(-9)/(-3) =3`

For -9 and -27

`r=(-27)/(-9) =3`

The ratio is always the same, so Carter's sequence is a geometric one.

Dominique -1, -3,-9, -81,...

For -1 and -3

`r=(-3)/(-1) =3`

For -3 and -9

`r=(-9)/(-3) =3`

For -9 and -81

`r=(-81)/(-9) =9`

The ratio is not the same, so Dominique's sequence is not a geometric one.