L4 · Describing the change from term to term

Learning goal

“I can describe how a sequence changes from term to term using operations - like 'add 6 each time' or 'multiply by 2 each time' - and I can use the change to find the next term.”

Increase — to get bigger. A sequence increases when each term is larger than the one before it.

Decrease — to get smaller. A sequence decreases when each term is smaller than the one before it.

Double — to multiply by 2. Doubling 12 gives 24. A sequence can change by doubling each time.

Halve — to divide by 2, splitting into two equal parts. Halving 12 gives 6. A sequence can change by halving each time.

Worked example

Describe the change in 11, 17, 23, 29. Step 1: Subtract neighbours: 17 − 11 = 6. The first jump is +6. Step 2: Check every jump: 23 − 17 = 6 and 29 − 23 = 6. The jump never changes. Step 3: Describe it: "add 6 each time." Use it: the next term is 29 + 6 = 35. For a shrinking sequence it works the same way: 50, 45, 40, 35 has jumps of −5, so the change is "subtract 5 each time." Say it plainly: a change is only THE change if it works for EVERY jump. Checking one jump is not enough.

Check yourself — explain it

How do you find the change in 8, 15, 22, 29?

Paired problem — example still visible

Describe the change and give the next term: 31, 28, 25, 22. -> Subtract 3 each time (31 − 28 = 3, and it stays 3); next term 19

Faded completion — last step is yours

"In 4, 13, 22, 31, the change is add ___ each time, so the next term is ___." -> 9; 40

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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