Sequence/ number series

Question

How do you solve number series or sequence where the values alternate between adding a number and subtracting a number?

For example: Find the 30th term in the sequence.

6,2,7,3,8,4,9..

Notice the complex pattern is subtracting 4 then adding 5. How do I go about finding the rule so that I am able to find any term number asked for? What are these kind kind of sequence specifically called?

Answer 1

You start by setting the first term of the sequence a_0=6. Then for the general term of the sequence a_n we have the following rule

a_n=a_{n-1}-4 if n is odd and

a_n=a_{n-1}+5 if n is even.