What Is the Value of 'a' in the Infinite Geometric Series?

[lionel messi.]

Sequences and series help...

1. Homework Statement
3+3a+3a^2+...∞ is = to 45/8 where a>0,then a is...?


3. The Attempt at a Solution
since it is a g.p so using
S=(a(rn-1))/(r-1) for r>1
ive all the values except for "n"..can someone help...:/

 

[eumyang]

S=(a(rn-1))/(r-1) for r>1
ive all the values except for "n"..can someone help...:/

Wrong formula. This is an infinite geometric series, so use
$$a + ar + ar^2 + ar^3 + ... = \frac{a}{1 - r}$$

 

[lionel messi.]

thanks..

 

[Villyer]

n is the number of terms, so in this case there are infinite terms.
As n tends to infinity, what does r^n tend to? (Assuming -1<r<1)
This gets you to the formula that eumyang posted.