What are the formulaes for:
Arithmatic progression, if i know how many numbers there are, their sum, and their product?
and
Geometric progression, if i know the second term and the sum to infinity?
First of all I think we need to know the first term and common difference." Arithmatic progression, if i know how many numbers there are, their sum?":
With that we could tell you the formula, but I think its better you consult your text book. Text books generally have a flow that makes it easy to understand, remember and apply.
I am sorry, this could be hard. I have no idea of this."and their product?"
I think its better if you post a problem that demands the use of these formulae. Can you post one?
Afterthought: I think you have a problem at hand and thus you want to know the formulae. So could you post those exactly as in the question?"and Geometric progression, if i know the second term and the sum to infinity?"
Assume that they are consecutive numbers... $\displaystyle a ~,~b~,~c$, in an arithmetic sequence of constant progression r.
$\displaystyle b=a+r$ and $\displaystyle c=a+2r$
$\displaystyle 18=a+b+c=3a+3r \implies {\color{red}a+r}=6 \quad a=6-r$
$\displaystyle 120=abc=a({\color{red}a+r})(a+2r)=a*6*(6+r)=6*(6-r)(6+r)$
$\displaystyle \implies 20=36-r^2 \implies r^2=16$
etc.
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A slightly different way is to write :
$\displaystyle a=b-r$, $\displaystyle c=b+r$
$\displaystyle 18=a+b+c=b-r+b+b+r=3b \implies b=6$
$\displaystyle 120=abc=(6-r)6(6+r) \implies 20=36-r^2$
etc