Question

Determine whether or not each of the following sequences is a geometric sequence. Check all that apply. A -48, 96, -192, 384 B … 1, 4, 9, 16 C ... 3, 9, 27 81 … D 5, 10, 20, 40, … F. 24, 20, 16, 12, … G. 25, 20, 15, 10, …

Answer 1

Answer: A. , C. and D.

Explanation:

We know that a geometric sequence is a sequence of numbers that is in a pattern where the next term is obtained by multiplying by a constant known as the common ratio.

A -48, 96, -192, 384

here,
`(96)/(-48)=(-192)/(96)=(384)/(-192)=-2`

hence, it is a geometric sequence.

B … 1, 4, 9, 16

here,
`(4)/(1)\\eq(9)/(4)`

hence, it is not a geometric sequence.

C ... 3, 9, 27 81 …

here,
`(9)/(3)=(27)/(9)=(81)/(27)=3`

hence, it is a geometric sequence.

D 5, 10, 20, 40, …

here,
`(10)/(5)=(20)/(10)=(40)/(20)=2`

hence, it is a geometric sequence.

F. 24, 20, 16, 12, …

here,
`(20)/(24)=(5)/(6)\\eq(16)/(20)=(4)/(5)`

hence, it is not a geometric sequence.

G. 25, 20, 15, 10, …

here,
`(20)/(25)=(4)/(5)\\eq(15)/(20)=(3)/(4)`

hence, it is not geometric sequence.