Question

Determine whether each sequence is an arithmetic sequence. Write yes or no. Explain. 7, 10, 13, 16, ...​

Answer 1

The given sequence is an arithmetic sequence.

Explanation:

Given sequence is:

7, 10, 13, 16, ...

Here

`a_1 = 7\\a_2 = 10\\a_3 = 13\\a_4 = 16`

In order for a sequence to be an arithmetic sequence the common difference between the consecutive terms of the sequence should be same. Common difference is denoted by d.

So,

`d = a_2 - a_1 = 10-7 = 3\\d = a_3 - a_2 = 13-10 = 3\\d = a_4-a_3 = 16-13 = 3`

As we can see that the common difference is same for consecutive terms.

The given sequence is an arithmetic sequence.