Arithmetico-geometric series
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An arithmetico-geometric series is the sum of consecutive terms in an arithmetico-geometric sequence defined as: , where
and
are the
th terms of arithmetic and geometric sequences, respectively.
Finite Sum
The sum of the first n terms of an arithmetico-geometric sequence is , where
is the common difference of
and
is the common ratio of
. Or,
, where
is the sum of the first
terms of
.
Proof:
Let represent the sum of the first n terms.