IB — mathsStandard1 min read

Geometric Sequences and Series

Master geometric sequences and series for IB Maths. Find terms, sums, and the sum to infinity.

Tutor AI Team2026-02-25T02:06:13.268Z

Geometric sequences have a constant ratio between consecutive terms. The sum to infinity is a key concept for IB Math.

Core Formulas

$u_n = u_1 \cdot r^{n-1}$ — nth term

$S_n = \frac{u_1(1-r^n)}{1-r}$ — sum of first $n$ terms ( $r \neq 1$ )

$S_\infty = \frac{u_1}{1-r}$ — sum to infinity ( $|r| < 1$ )

Problem

$u_1 = 3$ , $r = 2$ . $u_6 = 3 \cdot 2^5 = 96$ . $S_6 = \frac{3(1-64)}{1-2} = 189$ .

Solution

Problem

$u_1 = 100$ , $r = 0.8$ . $S_\infty = \frac{100}{0.2} = 500$ .

Solution

Problem

£5000 at 4% p.a. for 10 years: $5000 \times 1.04^{10} = £7401.22$ .

Solution

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#ib#maths#algebra#sequences#geometric

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