Algebra · Sequences
Chapter 1 · 4
The idea
The nth term of a quadratic sequence
Why constant SECOND differences signal an n² rule, why the n²-coefficient is HALF the second difference, and the subtract-and-conquer routine that finds the full an² + bn + c.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Sequences
The nth term of a quadratic sequence
Why constant SECOND differences signal an n² rule, why the n²-coefficient is HALF the second difference, and the subtract-and-conquer routine that finds the full an² + bn + c.
Why it works
The second difference is the fingerprint
When first differences aren't constant but keep changing by the same amount, the sequence is quadratic. For : differences — climbing by 2 each time. That constant second difference is the fingerprint of an term.Why you halve it
Watch itself: has differences and second difference 2. Scaling to scales the second difference to . SoKeep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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