Look at the number provided within the sequence. For example: What is the nth term in the sequence 5, 9, 13?
Calculate the differences between the numbers. When possible place the differences between the sequential numbers between those in the pattern. For example: 5 (+4), 9 (+4), 13.
Determine any patterns within the sequence. The difficulty in find the nth term comes from how clear the pattern is with some sequences being obvious while others may require multiple steps between the numbers. For example: 4 is added to each number in the sequence (as 1 + 4 = 5, + 4 = 9, and so on) so the nth number will be 4 higher than the previous number, plus 1 because the pattern starts at 1.
Write out the change between the sequenced numbers as an expression of n. The expression must be written so that any number in the sequence can be found using this expression. For example: the nth number of the sequence is 4n + 1
Check your expression by substituting a number for n. For example: The 6th number in the sequence makes the expression 4(6) + 1 or 25. The 10th number in the sequence is 4(10) + 1 or 41.
Write out the pattern to verify those numbers. This is an optional step but good for making sure the work is correct. For example: 5, 9, 13, 17, 21, 25, 29, 33, 37, 41. Notice that the 6th and 10th numbers in the sequence match those given by the expression.