Continuing a Pattern

Look at 2, 5, 8, 11. Each number is 3 more than the one before it. A list of numbers that follows a rule like this is a sequence, and each number in it is a term. To continue it, apply the same step once more: the next term is 11 + 3, which is 14.

To find the step, subtract each term from the next one: 5 - 2, 8 - 5 and 11 - 8 are all 3. Checking every gap, not just the first, is what tells you the pattern really is steady.

A sequence can go down too. In 40, 35, 30, each term is 5 less than the one before, so the next is 30 - 5, which is 25. On the board, write the next term t as the last term plus the step, then work it out.