## College Algebra (6th Edition)

A recursion formula defines how to obtain the next term if we know the preceding term(s). So, instead of defining the terms as a function of n, they are defined as a function of previous term(s). The form is $a_{n+1}=$( expression involving $a_{1},...,a_{n})$ Example: $\left\{\begin{array}{ll} a_{1}=3 & \\ a_{n+1}=a_{n}+2, & n \geq 1 \end{array}\right.$ defines a sequence with terms $a_{1}=3$ $a_{2}=3+2=5$ $a_{3}=5+2=7$ $... etc$ 3, 5, 7, 9,... The above sequence can be defined as as a function of n by defining the general term with $a_{n}=2n+1$