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nth Term of a Linear Sequence

When asked to find the n-th term of a linear sequence, you are asked to find the rule or the formula that allows you to find any term in the sequence.

This formula is of the form an + b; where the following criteria must be met:

  • a‘ is any positive or negative number (but not 0)
  • b‘ is any positive or negative number (can be 0)
  • n‘ must be a positive integer (whole number)

To find the n-th term for a sequence you need to go through a few steps. Suppose you have the following

STEP 1: Find the increase from term to term (+3 in this case)

STEP 2: List the correponding times table above the sequence ( 3 times table in this case)

STEP 3: Find the difference between terms in the 2 sequences

STEP 4: The nth term formula for this sequence is therefore

Example 2

You can also have a sequence that decreases in order. Here is an example

Given the sequence above, the steps to find the nth term are listed below.