A geometric series
is the sum of a geometric sequence.
a + ar + ar2 + ar3 + ar4 + ...
where r ≠ 0
is the common ratio and a
is a scale factor, equal to the sequence's start value.
3 + 6 + 12 + 24 + 48 +... is a geometric serie because each term is obtained by multiplying the preceding number by 2.
To solve exercises using geometric sequences you need the following formulas:
Given , find S7
This is a geometric serie with a common rate r=3.
Determine the sum of the first
12 terms of the geometric sequence where
the first terms are: -1,2,-4,8,...