Grade 7 Number Patterns Worksheets — Common Difference and Ratio PDF
By Grade 7 sequences run in both directions. Arithmetic rules can subtract as well as add, geometric ratios stretch to 5, and decreasing geometric sequences ask students to divide their way down. Naming the rule precisely — the common difference or the common ratio — is the language students carry into algebra.
Choose the skill and its level, set the number of problems with the stepper, and the sheet rebuilds instantly; add the answer key on its own page, then print or download a clean PDF. Because the link reproduces the identical worksheet, the same sheet works for a class handout today and a retest next week.
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Number Patterns · Grade 7
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Grade 7 · 2 pages · A4More Grade 7 number patterns skills
Each one generates a different kind of question, with its own three levels and answer key.
- Continue the SequenceWork out the rule from the terms shown, then write the ones that come next.
- Find the Missing TermThe gap is inside the sequence, so the rule has to be read from both sides of it.
- Name the RuleRead a sequence and write, in words, what its rule does at every step.
- Doubling and HalvingRuns that double at every step, and the same runs read backwards.
- Two Rules TogetherPatterns where two different jumps take turns, one term at a time.
- Multiplying SequencesSequences that grow by a fixed ratio each step, and the same runs in reverse.
What each level generates
Grade 7 continue the sequence — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Count on in equal steps
- Level 2Count back in equal steps
- Level 3Steps that grow
Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →
What Grade 7 number patterns should cover
Most curricula extend Grade 7 students to sequences that decrease as well as increase: arithmetic sequences with a negative common difference (450, 405, 360) and geometric sequences that divide, alongside multiplying ratios as large as 5. The vocabulary firms up here — common difference for the constant added, common ratio for the constant multiplier — and students are expected to use it.
Multiplying Sequences is the intended page, with Continue the Sequence as a warm-up and Doubling and Halving in between. A solid benchmark: a 12-problem sheet in ten to twelve minutes, the rule and its direction ('take away 45', 'times 4') noted beside each sequence, with at most one or two slips.
The errors Grade 7 sequences expose
Two mistakes dominate. On decreasing arithmetic sequences, students add the common difference back out of habit or lose a sign crossing zero into negatives; reading the sequence aloud in the direction it runs helps. On geometric sequences they confuse dividing with subtracting — 360, 120, 40 divides by 3, it does not take away a fixed amount — so the two-pair check (does one rule fit both gaps?) stays essential.
Interleave across sessions rather than inside one: each page is a single family on purpose, and a run of nothing but Multiplying Sequences teaches matching to the page, not the rule. Alternate it with Continue the Sequence and Two Rules Together, and insist students classify first, find the exact rule, then fill the blanks. Shuffle supplies endless fresh sets, and the easy-read font in the controls helps students who lose their place in longer sequences.
Frequently asked questions
▸What are common difference and common ratio?
The common difference is the fixed amount an arithmetic sequence adds each step; the common ratio is the fixed amount a geometric sequence multiplies by. Grade 7 expects students to find and name both from the terms.
▸Do Grade 7 patterns include decreasing sequences?
Yes, at the second level of four skills: Count back in equal steps on Continue the Sequence, Halve it each time on Doubling and Halving, Thirds: use the rule for term n on Multiplying Sequences, where each term comes from a rule that divides by a power of 3, and Rules that count back on Name the Rule; about half the two-gap sequences on Find the Missing Term count back too. Students work patterns in the shrinking direction, not just the growing one.
▸How is a decreasing geometric sequence different from a subtracting one?
A subtracting sequence takes away the same amount each time (30, 22, 14 subtracts 8); a decreasing geometric sequence divides by the same amount (48, 24, 12 divides by 2), so the gaps shrink rather than stay equal.
▸Can students mark their own work?
Yes — tick the answer key box and a numbered key prints on its own final page. Hand it out after the attempt and have students locate the exact term where a sequence went wrong, which is strong pattern reasoning in itself.
▸Is this generator free for classroom use?
Completely — no account, no watermark, no limit on sheets. Share one link so every student gets the identical page, or Shuffle to hand neighbouring desks different problems at the same settings.