Question

Can someone please explain how do I find the sum on this?

Answer 1

\[\sum_{k=1}^{10} 3^{k}\]

Answer 2

How do I know what is r and a?

Answer 3

Sure, there's a closed-form formula for this:
\[
\frac{a(1-r^{n})}{1-r}=S
\]So, we have that our \(a\) or initial term is \(3^1=3\), and our last term is at \(n=10\), while our common ratio is 3, hence:
\[
\frac{3(1-3^{10})}{1-3}=S
\]It's pretty ugly, but solvable.

Answer 4

How did you figure out the common ratio?

Answer 5

The common ratio is defined as:
\[
a=\frac{l_{n+1}}{l_n}
\]Or, it can also be seen as the base for the exponent in the sum.

Answer 6

so to get the first and the second term you would plug in k=1 and k=2, and than divide them to get r?

Answer 7

Sure, if you want to. But, if you have the actual sum, \(a\) is simply the base of the exponent.

Answer 8

ok, so if instead of \[3^{k}\] I have lets say \[(-1/2)^{k+1}\] my common ration would be -1/2?

Answer 9

Yep.

Answer 10

ok, I think i got it now. Thanks for your help!

Answer 11

Sure thing.