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

Solution:

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

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

B. 1,2,4,8,16

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

C.-3,1,5,9

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

D. 4,8,24,96,480

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

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