Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Series — Arithmetic, Geometric & Binomial

15 min read

Arithmetic and geometric sequences and series, sums to infinity, and the binomial expansion.

A series is the sum of a sequence. Three types appear on the paper.

Arithmetic series

Common difference $d$ . The $n$ th term and sum: $u_n = a + (n-1)d \qquad S_n = \frac{n}{2}\big(2a + (n-1)d\big)$

Worked example. For $3, 7, 11, \dots$ ( $a = 3, d = 4$ ): $u_{10} = 3 + 9(4) = 39$ ; $S_{10} = \tfrac{10}{2}(6 + 36) = 210$ .

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.

Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

15 min read

Arithmetic and geometric sequences and series, sums to infinity, and the binomial expansion.

A series is the sum of a sequence. Three types appear on the paper.

Common difference $d$ . The $n$ th term and sum: $u_n = a + (n-1)d \qquad S_n = \frac{n}{2}\big(2a + (n-1)d\big)$

Worked example. For $3, 7, 11, \dots$ ( $a = 3, d = 4$ ): $u_{10} = 3 + 9(4) = 39$ ; $S_{10} = \tfrac{10}{2}(6 + 36) = 210$ .

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.