# S-Cool Revision Summary

## S-Cool Revision Summary

#### Sequences and Series

A **Sequence** is a list of numbers connected by a rule.

A **Series** is the sum of a sequence

**There are two main types of series:**

Arithmetic Progressions and Geometric Progressions.

#### Arithmetic Progressions

**Arithmetic Progressions** have a common difference between each term.

n^{th} term = a + (n - 1)d, where a = first term, and d = common difference.

**The sum of the first n terms is:**

, pairs each totalling (a + l) - (the sum of the first and last terms.)

**This can be rewritten using the formula for the n ^{th} term to get:**

#### Geometric Progressions

**Geometric Progressions** have a common ratio (multiple) between each term.

n^{th} term = ar^{n-1} , where a = first term, and r = common ratio

**The sum of the first n terms is:**

**or**

This is the sum to infinity and this sum only converges when:

The **Arithmetic mean** of two numbers (m and n) =

The **Geometric mean** of two numbers =