Maths - Series | Olly Britton

Flashcards

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?

\[ \vert r \vert < 1\]

What must be true about $r$ for a divergent geometric series?

\[ \vert r \vert > 1\]

What is the formula for the sum of a convergent geometric sequence with $ \vert r \vert < 1$?

\[\frac{a}{1 - r}\]