Question

Please help, the sooner the better :)

Answer 1

57

Answer 2

What is the sum of the geometric series?

Answer 3

-.- very funny

Answer 4

LOL!

Answer 5

\(\large {
\textit{sum of geometric sequence}=S{\color{brown}{ n}}=a_1\left( \cfrac{1-r^{\color{brown}{ n}}}{1-r} \right)\qquad\\ \quad \\ \Sigma_{n=1}^{10}\quad 6(2)^{\color{brown}{ n}}
\\ \quad \\
a_1\to \textit{first term of sequence}
}\)

Answer 6

oh dear, many numbers and letters... ok...

Answer 7

so in this case since n = 10
then \(\bf S_{\color{brown}{ 10}}=a_1\left( \cfrac{1-r^{\color{brown}{ 10}}}{1-r} \right)\)

Answer 8

oh ok that makes a bit of sense

Answer 9

so am I trying to figure out what S is?

Answer 10

ohh S is jus the notation for "S"um

Answer 11

I'm already confused :(

Answer 12

another way of saying
if we have "n" terms, beginning at \(a_1\)
the "S"um of it will be this

Answer 13

oh ok, then why does it have base 10?

Answer 14

it is not a base
yes, it looks like that because is a subscript of the letter
is just a way to say "a sum that goes up to "n"th number"

Answer 15

ah ok

Answer 16

hmmm actually
we haven't plugged in "r"
one sec

Answer 17

ok

Answer 18

I have to go, please continue to explain and I will read it when I come back

Answer 19

\(\large { \bf
\textit{sum of geometric sequence}=S_{\color{brown}{ n}}=a_1\left( \cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}} \right)
\\ \quad \\
\qquad a_1\to \textit{first term of the sequence}
\\ \quad \\

\Sigma_{{\color{brown}{ n}}=1}^{10}\quad 6({\color{blue}{ 2}})^{\color{brown}{ n}}\implies
S_{\color{brown}{ 10}}=a_1\left( \cfrac{1-{\color{blue}{ 2}}^{\color{brown}{ 10}}}{1-{\color{blue}{ 2}}} \right)
}\)