# Arthimetic and Geometric

#### dwsmith

##### Well-known member
Is it true that geometric progressions are \leq arithmetic?

#### Fantini

MHB Math Helper
Doesn't seem a far shot. We know that arithmetic mean is greater or equal than geometric mean, perhaps applying that you could get to your result. Are we assuming finiteness or not?

#### Sudharaka

##### Well-known member
MHB Math Helper
Is it true that geometric progressions are \leq arithmetic?
Hi dwsmith, Can you please clarify your question a bit more. Do you mean the inequality of arithmetic and geometric means ?

Kind Regards,
Sudharaka.

#### dwsmith

##### Well-known member
I am wondering if GP $\leq$ AP

#### Sudharaka

##### Well-known member
MHB Math Helper
I am wondering if GP $\leq$ AP
So your question seems to be whether the sum of any arithmetic progression is greater than or equal to the sum of any geometric progression. That is not the case. For example, $$1,\,3,\,5$$ is an arithmetic progression and $$2,\,4,\,8$$ is a geometric progression. But, $$1+3+5=9\mbox{ and }2+4+8=14$$

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