Algebra · Sequences
Chapter 1 · 3
The idea
The nth term of a linear sequence
Why a constant difference makes a sequence "dn + something", how the zeroth term pins down the constant, and how the nth term answers "is 122 in this sequence?" with an equation instead of a hunch.
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 linear sequence
Why a constant difference makes a sequence "dn + something", how the zeroth term pins down the constant, and how the nth term answers "is 122 in this sequence?" with an equation instead of a hunch.
Why it works
Two kinds of rule
Exam papers ask two things about : "find the nth term" and "is 122 a term of this sequence?" — and the second is unanswerable by listing terms until your hand aches. The nth term turns it into a one-line equation. A linear (arithmetic) sequence climbs by the same amount each step — this one adds 4 every time — and two different kinds of rule describe it:- the term-to-term rule — "add 4" — tells you how to get the NEXT term;
- the nth term — a formula in — hands you ANY term directly.
Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.