Question

In the arithmetic sequence {13, 6,-1,-8,...}, what is the common difference?

Answer 1

Answer:  -7

Explanation:

Pick any term. Subtract off the previous one to find the common difference.

• term2 - term1 = 6-13 = -7
• term3 - term2 = -1-6 = -7
• term4 - term3 = -8-(-1) = -8+1 = -7

And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.

We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.