# Maths - Series

> Source: https://ollybritton.com/notes/a-level/maths/topics/series/ · Updated: 2021-09-18 · Tags: maths, school

## See Also
## Flashcards
### 2021-09-18
##### What's the format of a general arithmetic sequence term $U_n$ for common difference $d$ and start term $a$??
$$
U_n = (n - 1)d + a
$$

##### What's the formula for the sum $S_n$ up to term $n$ of a sequence with start $a$ and common difference $d$??
$$
S_n = \frac{n}{2}\left( (n - 1)d + 2a \right)
$$

##### What's the formula for the sum $S_n$ of an arithmetic sequence between terms $a$ and $l$??
$$
S_n = \frac{n}{2}\left( a + l \right)
$$

##### What does it mean for a geometric sequence to be divergent??
The terms get further and further apart.

##### What does it mean for a geometric sequence to be convergent??
The terms get closer and closer together.

##### What must be true about $r$ for a convergent geometric series??
$$
|r| < 1
$$

##### What must be true about $r$ for a divergent geometric series??
$$
|r| > 1
$$

### 2021-10-03
##### What is the formula for the sum of a convergent geometric sequence with $|r| < 1$??
$$
\frac{a}{1 - r}
$$

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