The idea

Geometric sequences and series

Sequences with a constant common ratio — the nth term, the sum of n terms, and the sum to infinity (and exactly when it exists).

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

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Pure · Sequences & series

Sequences with a constant common ratio — the nth term, the sum of n terms, and the sum to infinity (and exactly when it exists).

Fold a piece of paper in half, then in half again: the layers go

1, 2, 4, 8, \dots

Every step multiplies by the same number. That's a geometric sequence, and the multiplier is the common ratio

r

a,\ ar,\ ar^2,\ ar^3,\ \dots

Arithmetic sequences added a fixed step; geometric ones multiply by a fixed ratio — which is why they explode (or vanish) so much faster. Find

r

by dividing any term by the one before it:

r = \dfrac{u_2}{u_1}

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The rest of the explanation, plus 3 worked examples you step through move by move.

Takes a minute — no card.