Question

Which of the following is a geometric sequence?A. -5,0,10,25,45B. 1,2,4,8,16C.-3,1,5,9D. 4,8,24,96,480

Answer 1

We are required to determine which is a geometric sequence.

Firstly, let us look at what a Geometric sequence is .

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In summary, a Geometric sequence has a common ratio.

Let us take a look at the options one after the other

A. -5,0,10,25,45

`\begin{gathered} (0)/(5)\text{ = 0} \\ \\ (10)/(0)=\infty \\ there\text{ is no common ratio here, hence it is not a Geometric sequence} \end{gathered}`

B. 1,2,4,8,16

`\begin{gathered} (2)/(1)=2 \\ \\ (4)/(2)=2 \\ \\ (8)/(4)=2 \\ \\ (16)/(8)=2 \\ We\text{ can see that this sequence has a common ratio of 2, hence it is a geometric sequence} \end{gathered}`

C.-3,1,5,9

`\begin{gathered} (1)/(-3)=-(1)/(3) \\ \\ (5)/(1)=5 \\ There\text{ is no common ratio here, hence it is not a geometric sequence} \end{gathered}`

D. 4,8,24,96,480

`\begin{gathered} (8)/(4)=2 \\ (24)/(8)=3 \\ There\text{ is no common ratio here, hence it is not a geometric sequence} \end{gathered}`

Thus, the answer is B. 1,2,4,8,16