Cotangent

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:

a_{1}, a_{2}, a_{3}, ..., a_{n}, ...

The number a_{1} is called the first term, a_{2} is the second term, and in general a_{n} 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 a_{n}=3n+2, find a_{1}, a_{2}, a_{3} and a_{4}. By substituting n=1,2,3,4 in the general term of the sequence, we obtain:

a_{1}=3(1)+2=3+2=5 a_{2}=3(2)+2=6+2=8 a_{3}=3(3)+2=9+2=11 a_{4}=3(4)+2=12+2=14

Find the general term for the following sequences:

Solution: