Sequences and Series Cheat Sheet
0B
Arithmetic Sequences and Series
1B
Geometric Sequences and Series
Arithmetic sequences happen when you
add
numbers. The number added is called the
common
difference.
Geometric sequences happen when you
multiply
numbers. The number multiplied is called the
common ratio.
Recursive formula of an arithmetic sequence:
๐ข
๐
=๐ข
๐โ1
+๐
Recursive formula of a geometric sequence:
๐ข
๐
=๐โ๐ข
๐โ1
Explicit formula of a basic arithmetic sequence:
๐ข๐=๐ข1+(๐โ1)๐ ๐๐
๐ข๐=๐ข๐+๐๐
Explicit formula of a basic geometric sequence:
๐ข๐=๐ข1โ๐๐โ1
Partial sum of an arithmetic sequence:
๏ฟฝ๐ข๐=
๐
๐=1 ๐
2(๐ข1+๐ข๐) ๐๐
๏ฟฝ๐ข๐=๐๐ข1+๐(๐โ1)
2๐
๐
๐=1
Partial sum of a geometric sequence:
๏ฟฝ๐ข๐=๐ข1๏ฟฝ1โ๐๐
1โ๐ ๏ฟฝ
๐
๐=1
To input sums in the (TI-89 and similar) calculator:
โ(๐๐ฅ๐๐๐๐ ๐ ๐๐๐,๐ฃ๐๐๐๐๐๐๐,๐๐๐ก๐ก๐๐ ๐๐๐ข๐๐,๐ก๐๐ ๐๐๐ข๐๐)
