An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive numbers is the same.

The difference between consecutive terms is called the common difference.

Let's construct our own arithmetic sequence. I will choose the start to be \(7\) and the common difference to be \(4.\)

The first term is \(7\) since that is where I chose to start. The next terms if \(4\) more than \(7\) since \(4\) is the common difference. That is \(11.\) The next number after that is \(4\) more than \(11.\) That is \(15.\) Then comes \(4\) more than \(15,\) which is \(19.\)

We can keep going and write out the first terms of the sequence: \[7,11,15,19,23,27,31,35,\dots\]

Here is a sequence: \[6,8,10,12,14\] Find the next three terms.

This sequence starts at \(6\) and every other term is \(2\) greater than the term that comes before it. So, this is an arithmetic sequence with a common difference of \(2.\)

The last term we are given is \(14.\) The next term is \(2\) more. So, the next term is \(16.\) The next after that is \(2\) more, which is \(18.\) The third term is \(2\) more than \(18,\) which is \(20.\)

We have found the next three terms: \[16,18,20\]