Video: Writing the Following Terms in a Given Arithmetic Sequence

Video Transcript

Write the next three terms of the arithmetic sequence: three point three, four point two, five point one, six. In an arithmetic sequence, the difference between one term and the next is constant.

In other words, we add the same value each time infinitely. How do we know what is being added each time? Or perhaps what is the difference between each of these terms? We can quickly ask what is six minus five and one-tenths, which is nine-tenths. You add nine-tenths to five and one-tenths to equal six. If this is truly an arithmetic sequence, then we would be adding nine-tenths to each term to get the next term. But because we sometimes make mistakes, let’s just check to make sure.

Just three and three-tenths plus nine-tenths equals four and two-tenths. It does. And four and two-tenths plus nine-tenths equals five and one-tenths. Now that we figured out the constant that’s being added each time, we’ll need to determine the next three spaces: six plus nine-tenths equals six and nine-tenths. When you add nine-tenths to that, we get seven and eight-tenths plus nine-tenths again is eight and seven-tenths. The next three terms in our arithmetic sequence are six and nine-tenths, seven and eight-tenths, eight and seven-tenths.