L4 · Sequences Clinic: Missing Terms and New Sequences

Learning goal

“I can find missing terms anywhere in an arithmetic sequence - including across a gap of several steps - find a term at a given position using a rule or extension, create new arithmetic sequences from a description, and solve problems involving arithmetic sequences.”

Gap (in a sequence) — one or more missing terms in a row. The total change across a gap must be shared equally among its steps.

Extend — to continue a sequence beyond its given terms by repeatedly applying the constant difference.

Create a sequence — to build a new sequence from a starting term and a constant difference (or from a rule).

Worked example

Find the missing terms: 7, __, __, 22. Step 1: Count the STEPS from 7 to 22: 7 -> blank -> blank -> 22 is 3 steps. Step 2: Total change: 22 - 7 = 15. Shared equally over 3 steps: 15 / 3 = 5 per step. The constant difference must be +5. Step 3: Fill: 7, 12, 17, 22. Check: gaps 5, 5, 5 - and the last gap lands exactly on 22, which proves the sharing was right. Say it plainly: a wide gap is just several constant differences stacked. Divide the total change by the number of steps, then walk.

Check yourself — explain it

In 5, __, __, 20, the per-step change is found by...

Paired problem — example still visible

3, __, __, 18 -> total change 15 over 3 steps = 5 per step -> 3, 8, 13, 18

Faded completion — last step is yours

"10, __, __, 25: change 15 over 3 steps = 5 per step, so the terms are 10, 15, ___, 25" -> 20

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

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