College Algebra & Trigonometry, 2018a

6.1. SEQUENCES 289
Finding a general or recursive definition for a sequence can be trickier than just
writing out the terms. Common things to look for -
Is this an alternating sequence? That is, do the terms bounce back and forth
between positive and negative values. If so, then you will need to include (−1) n
or (−1) n+1 in your general term.
Example: {−1, 2, −3, 4, ...}
a n =(−1) n (n)
or
a 1 = −1
a n =(−1)(a n−1 )+(−1) n
Is there a common difference between the terms? If so, then the sequence behaves
much like a linear function and will have a form similar to y = mx + b, where m
is the common difference.
Example: {5, 8, 11, 14, ...}
a n =3n +2
or
a 1 =5
a n = a n−1 +3