A sequence is an ordered list of numbers:
3, 6, 9, 12, .... 1, 3, 5, 7, ...
A sequence can be thought of as a list of numbers written in a definite order:
a1, a2, a3, ..., an, ...
The number a1 is called the first term, a2 is the second term, and in general an is the nth term.
The terms of a sequence often follow a particular pattern. In those instances, we can determine the general term that expresses every term of the sequence. For example:
Given an=3n+2, find a1, a2, a3 and a4. By substituting n=1,2,3,4 in the general term of the sequence, we obtain:
a1=3(1)+2=3+2=5 a2=3(2)+2=6+2=8 a3=3(3)+2=9+2=11 a4=3(4)+2=12+2=14
Find the general term for the following sequences:
Solution:
