Question

Arithmetic Sequence? The first four terms of a sequence are given. Can these terms be the terms of an arithmetic sequence? If so, find the common difference.

$-31,-19,-7,5,\dots$

Short answer

Yes, the given sequence is an arithmetic sequence with a common difference $12$.

Step-by-step solution

Step 1. Given information.

The given sequence is:

$-31,-19,-7,5,\dots$

Step 2. Write the concept.

A sequence is called an arithmetic sequence if the difference between consecutive terms is constant.

Step 3. Determine the difference between consecutive terms.

The difference between consecutive terms:

$\begin{array}{l}-19-\left(-31\right)=-19+31\\ =12\\ -7-\left(-19\right)=-7+19\\ =12\\ 5-\left(-7\right)=5+7\\ =12\end{array}$

Since the difference between consecutive terms is constant, therefore the given sequence is an arithmetic sequence with a common difference $12$.