Question

Identify the following sequence as geometric, arithmetic, or neither 1, 3, 7, 15, 31

Answer 1

Arithmetic sequences have a common difference while geometric sequences have common ratio.

Let's check whether the terms have a common difference.

`\begin{gathered} 31-15=16 \\ 15-7=8 \\ 7-3=4 \\ 3-1=2 \end{gathered}`

As we can see, each term doesn't have the same difference, hence, they don't have a common difference and thus, the given is not an arithmetic sequence.

Now, let's check whether they have a common ratio by dividing the term by its previous term.

`\begin{gathered} 31/15=2.0667 \\ 15/7=2.1429 \\ 7/3=2.3333 \\ 3/1=3 \end{gathered}`

As we can see above, they don't have a common ratio, hence, the given is not a geometric sequence.

Therefore, the given sequence is neither arithmetic nor geometric sequence.