Video Transcript
Write the next three terms of the
arithmetic sequence:3.3, 4.2, 5.1, 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.
