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An arithmetic sequence (sometimes called a “progression”) is a particular type of sequence that has an initial value, as with all sequences. A proper arithmetic sequence has a common difference, that when added to the initial number and each consecutive number, provides the arithmetic sequence. Keep in mind that this common difference can be a positive or a negative value so the arithmetic sequence might be increasing or decreasing regularly. In addition, an arithmetic sequence may begin with a negative number as long as the sequence progresses by the constant value from that starting point.

An arithmetic sequence example would look like this:

1, 5, 9, 13, 17, 21, 25, 29, … with a common difference of 4.

Look for the common difference by subtracting the preceding value from the current value and ensuring this holds for the following numbers.

### Instructions

1.

Is this sequence an arithmetic sequence? 2, 1, 3, 4, 7, 11, ….

Assign "yes" or "no" to checkpoint_1.

2.

If we have 1, 4, 7, 10, 13, 16, 19, 22, 25, …, what is the number following “25?”

Assign the answer to checkpoint_2.