1. ## Geometric Series

Hello, I've been trying to solve this problem: "How many generations must a person go back to have at least 1000 ancestors?"

I've been trying ways to do it.. but not sure how. I know that the series goes like 2 + 4 + 8 and so on, so I know my a=2 and r=2. Don't really know where to go from there though. The question says at least 1000, so 1000 isn't a value I can plug into my equation.

Not asking for anyone to solve, maybe just point me in the right direction on how to start. Thank you!

2. $\displaystyle S_n = \frac{a(1-r^n)}{1-r}$

$\displaystyle 1000 \geq \frac{2(1-2^n)}{1-2}$

solve for n.

3. Originally Posted by pickslides
$\displaystyle S_n = \frac{a(1-r^n)}{1-r}$

$\displaystyle 1000 \geq \frac{2(1-2^n)}{1-2}$

solve for n.
So I got this: $\displaystyle 2^n \leq 501$
Is that right? I don't get how I find n.

4. Given your arithmetic is correct then

$\displaystyle 2^n \leq 501$

$\displaystyle n \leq \log_2(501)$

or if you don't like/know logs you can use trial and error on n.