Question

In your own words, explain how to determine whether a sequence is an arithmetic.

Short answer

We have to find the common difference between consecutive terms.

Step-by-step solution

Step 1. Introduction of sequence.

Consider that there is a sequence that is defined as:

$a_1+a_2+a_3+\cdots +a_n$

Let's consider that the above sequence is an arithmetic sequence.

Step 2. Explanation.

According to step 1, the sequence is an arithmetic sequence. So, the common difference of consecutive will be the same.

$\begin{array}{rcl}{a}_2-a_1& =& d\\ a_3-a_2& =& d\\ a_n-a_{n-1}& =& d\end{array}$

Thus, by finding the common difference, we can identify whether the given sequence is an arithmetic sequence or not.