Question

hi. how do you find n mathematically for a question like: find the sum of the finite geometric series -5-10-20-40-...-2560

Answer 1

There are formulas for all types of geometric progression
Easily available online

Answer 2

well the formula i have is s=a1(1-r^n)/1-r, but i don't understand how to find n...

Answer 3

if you know r and s .... its just algebra

Answer 4

even if you dont know them ... its still algebra :)

Answer 5

you don't know s. you're trying to find the sum

Answer 6

\[S_n=a_1\frac{1-r^n}{1-r}\]
\[S_n\frac{1-r}{a_1}=1-r^n\]
\[r^n=1-S_n\frac{1-r}{a_1}\]
\[log~r^n=log\left(1-S_n\frac{1-r}{a_1}\right)\]
\[n~log~r=log\left(1-S_n\frac{1-r}{a_1}\right)\]
\[n=\frac{log\left(1-S_n\frac{1-r}{a_1}\right)}{log(r)}\]

Answer 7

so your trying to find out the number of terms in order to find the sum, thats a different thing

Answer 8

yeah im trying to find the sum

Answer 9

you have to use the explicit formula, not the sumation formula

\[a_n=a_1~r^{n-1}\]
\[2560=5~(2)^{n-1}\]

Answer 10

so from there you solve for n?

Answer 11

yep

Answer 12

looks like n=2560(2/5) to me

Answer 13

ok ill do it that way thanks a ton for your help

Answer 14

youre welcome.