# Math Help - Just a quick one

1. ## Just a quick one

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?

2. Originally Posted by Nixietube
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?
" Arithmatic progression, if i know how many numbers there are, their sum?":
First of all I think we need to know the first term and common difference.

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.

"and their product?"
I am sorry, this could be hard. I have no idea of this.

I think its better if you post a problem that demands the use of these formulae. Can you post one?

"and Geometric progression, if i know the second term and the sum to infinity?"
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?

3. It doesn't give the first number in the series, just the sum of the three numbers, and the product. Sorry i don't have the question at hand

4. Are they consecutive numbers of the sequence ?

Can you write all down ?

5. The sum of 3 numbers in an arithmatic progression are 18 and their product is 120?

I found some formulaes, but most require you to know the first term

6. Originally Posted by Nixietube
The sum of 3 numbers in an arithmatic progression are 18 and their product is 120?

I found some formulaes, but most require you to know the first term
Assume that they are consecutive numbers... $a ~,~b~,~c$, in an arithmetic sequence of constant progression r.

$b=a+r$ and $c=a+2r$

$18=a+b+c=3a+3r \implies {\color{red}a+r}=6 \quad a=6-r$

$120=abc=a({\color{red}a+r})(a+2r)=a*6*(6+r)=6*(6-r)(6+r)$
$\implies 20=36-r^2 \implies r^2=16$

etc.

---------------------
A slightly different way is to write :

$a=b-r$, $c=b+r$

$18=a+b+c=b-r+b+b+r=3b \implies b=6$

$120=abc=(6-r)6(6+r) \implies 20=36-r^2$

etc

7. Thankyou!
When i went through it i ended u with 2,6,10
2+6+10 = 18
2x6x10 =120

Edit, just in case anyone else is doing something like this,
I re-arranged
20 = 36-r^2

To give
r^2 = 36 - 20

Therefore
r = 4

6+4 = 10
6-4 = 2

8. Therefore
r = 4
Uh-oh !
It can be r=-4

But it doesn't change anything ^^

For your geometric progression, do you have an example ?

9. I managed to stumble my way through the geometric progression one, but thankyou anyway moo, you've been a great help!