Class 3 to 11 · 26 games

Sequences, explained with pictures

Lists of numbers that follow a rule, and finding what comes next — or far ahead.

In everyday life: Squares in a growing pattern of tiles, seats in rows that grow by two, money saved doubling each month.

A pattern you can see is a pattern you can count

The first figure is made of 2 squares, the next of 5, the next of 8. The shape grows by the same 3 every time, and that 3 is the rule. Counting the squares in each figure turns a picture into a list of numbers you can carry on.

figure 1: 2 squares
figure 2: 5 squares
figure 3: 8 squares

Find the rule before you find the next term

Look at the step from one term to the next. If it is the same amount each time the sequence is arithmetic; if it is the same multiplier, it is geometric.

0615
Each step climbs by the same 4

A rule lets you jump ahead

Once you know the first term and the step, you can get the 50th term without writing out the 49 before it.

A worked example

What comes next: 3, 7, 11, 15, ...?

0620
The next point: 19

19

Each term is 4 more than the one before, so 15 + 4 = 19.

Words to know

rule
What the pattern does to get from one term to the next.
term
One number in the sequence.
common difference
The fixed amount added each time in an arithmetic sequence.
common ratio
The fixed multiplier in a geometric sequence.

In the games

You will carry a pattern on, say what each step does, and use that rule to jump to a term far past the end of the row.

Skills

  • Patterns and the rule behind them · Class 4
  • Arithmetic and geometric sequences · Class 10
  • Sums of arithmetic, geometric and square series · Class 11

By class

Practise sequences in Tivumo

No download, no account for your child. Classes 3 to 12, more than 1,000 games.