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GRADE 4 · ALBERTAOUTCOME AB-G4-4P1

L2 · Geometric Sequences: Constant Multiplicative Change

Learning goal

“I can recognize and build a geometric sequence - where each term comes from multiplying the term before by the same number every time - and I can tell it apart from an arithmetic sequence.”

Geometric sequence — a sequence where each term is found by MULTIPLYING the term before by the same number every step.
Multiplier — the constant number you multiply by at each step (the geometric sequence's constant change).
Doubling — multiplying by 2 each step: each term is twice the one before.
Halving — dividing by 2 each step: each term is half the one before. Halving is still a constant multiplicative change.
Worked example

Read the sequence: 3, 6, 12, 24, 48. Step 1: Try the L1 test - gaps: 6 - 3 = 3; 12 - 6 = 6; 24 - 12 = 12. The gaps are NOT constant, so this is not arithmetic. Step 2: Try multiplying: 3 x 2 = 6; 6 x 2 = 12; 12 x 2 = 24; 24 x 2 = 48. The multiplier is x2 at every step. Step 3: This is a geometric sequence: initial term 3, constant change multiply by 2. Say it plainly: arithmetic = same ADD every step; geometric = same MULTIPLY every step. One more fact from the curriculum: a geometric sequence never starts at 0 - multiplying 0 by anything stays 0, so the sequence could never grow.

Check yourself — explain it

To decide whether a sequence is geometric, you check...

Paired problem — example still visible

Find the multiplier and the next term: 2, 6, 18, 54, ___ -> Multiplier x3; next term 162 (54 x 3)

Faded completion — last step is yours

"Sequence: 4, 12, 36, 108. Each term is the one before x ___. The next term is 108 x ___ = ___" -> 3; 3; 324

Ready to practise?

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

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