Question

Four students wrote sequences during math class.

Andre - 3/4, 3/8, - 3/16, - 3/32..
Brenda 3/5, -3 /8, 3/16, 3/32..
Camille 3/4, 3/8, - 3/16, - 3/32..
Doug 3/4, - 3/8, 3/16, -3 /32..

Which student wrote a geometric sequence?
Andrea
Brenda
Camille
Doug

Answer 1

Doug because his sequence follows a rule of multiplying by -1/2 Hope I got it right for your sake.

Answer 2

Doug wrote geometric sequence.

Explanation:

a geometric sequence is where we get common ratio between consecutive terms

`\text{common ratio}=(a_2)/(a_1)`

In case of Andre:

On substituting the values so as to find common ratio is

`((3)/(8))/((3)/(4))=(-1)/(2)`

`((-3)/(16))/((3)/(8))=(-1)/(2)`

`((-3)/(32))/((-3)/(16))=(1)/(2)`

Andre did not write a geometric sequence.

In case of Brenda:

On substituting the values so as to find common ratio is

`((-3)/(8))/((3)/(5))=(-5)/(8)`

`((3)/(16))/((-3)/(8))=(-1)/(2)`

`((3)/(32))/((3)/(16))=(1)/(2)`

Brenda did not write a geometric sequence.

In case of Camille

On substituting the values so as to find common ratio is

`((3)/(8))/((3)/(4))=(1)/(2)`

`((-3)/(16))/((3)/(8))=(-1)/(2)`

`((-3)/(32))/((-3)/(16))=2`

Camille did not write a geometric sequence.

In case of Doug:

On substituting the values so as to find common ratio is

`((-3)/(8))/((3)/(4))=(-1)/(2)`

`((3)/(16))/((-3)/(8))=(-1)/(2)`

`((-3)/(32))/((3)/(16))=(-1)/(2)`

Doug wrote a geometric sequence.