The match mini game

SL 1.2 - Arithmetic Sequence and Series

What is an Arithmetic Sequence?

An arithmetic sequence is a sequence where the difference between consecutive terms is constant. This constant difference is called the common difference (usually denoted as d).

Key Formulas

For an arithmetic sequence with first term $u_{1}$ common difference $d$:

1. The nth term formula: $u_{n} = u_{1} + (n-1)d$

2. The sum of n terms: $S_n = \frac{n}{2}[2u_{1} + (n-1)d]$

Sigma Notation

The sum of a sequence can be written using sigma notation: $\sum_{k=1}^{n} u_{k}$

For arithmetic sequences, this equals $S_n$.