To find out approximately how many minutes students in a high school are spending texting while in class, the guidance counselor
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Check the forward differences of the sequence.
If , then let
be the sequence of first-order differences of
. That is, for n ≥ 1,
so that .
Let be the sequence of differences of
,
and we see that this is a constant sequence, . In other words,
is an arithmetic sequence with common difference between terms of 2. That is,
and we can solve for in terms of
:
and so on down to
We solve for in the same way.
Then
and so on down to