How do I find a1 for a geometric series when I'm only given Sn, an, and r?

Question

aum · Answer

$\Large S_n = a_1\frac{1-r^n}{1-r}$   ---- (1)

$\Large a_n = a_1 r^{n-1}$  ----- (2)

aum · Answer

From (2): $\Large a_n * r = a_1 r^{n}; ~~~r^n = \frac{a_nr}{a_1}$.  Put this in (1) and solve for $a_1$.

anonymous · Answer

Thanks, this helps a lot! One more question though, how did you get:
an * r = a1rn

aum · Answer

I multiplied both sides of (2) by r so that I can find $\large r^n$ that occurs in (1)

aum · Answer

$\Large a_n = a_1 r^{n-1}$
Multiply both sides by r:
$\Large a_n * r = a_1 r^{n-1} * r = a_1r^n$

anonymous · Answer

So when you multiply $$r^n-1 * r$$ , the -1 cancels out?

aum · Answer

$\large a^m * a^n = a^{m+n}$

$\large r^{n-1} * r^1 = r^{n-1+1} = r^n$