519f08da03
* Introduced Geometric progression * Fixed some typos and added geometric mean * fixed some more typos * Added Design Patterns book * added design pattern books
3.5 KiB
title
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| Geometric Series |
Geometric Series
A geometric progression is a sequence of numbers, whose first term is non zero and each term is obtained by multiplying its proceding term by a constant quantity. This constant quantity is called common ratio of the GP.
The sum of this progression is called geometric series.
We can say if a1,a2,a3,....,an are in GP then
is known as common ratio of GP.
if a is the first term then GP can be written as
example of a GP : 2,4,8,16,....
The nth term of GP (Also known as General term)
Let a be the first term, r be the common ratio and l be the last term of a GP, then nth term is given by
where
The sum of n terms of a GP
Let a be the first term, r be the common ratio and l be the last term of a GP, then sum of n terms is given by:
and is not defined for r=1
Geometric Mean
if we insert geometric mean between two numbers and
, then
Geometric mean =