Question

What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms?

Answer 1

\[\LARGE S_9=a_1\cdot \frac{1-q^9}{1-q}\]
and...
if a_1=4 ,a_2=12
\[\LARGE q={a_2 \over a_1}={12 \over 4}=3\]
so q=3

thus...
\[\LARGE S_9=4\cdot \frac{1-3^9}{1-3}\]
I think this should be :)

Answer 2

is it in the formula a1(1-r^n) / 1-r

Answer 3

this:
\[\LARGE Sn=a_1\cdot {1-r^n \over 1-r}\] it's the same as:
\[\LARGE Sn=a_1\cdot {1-q^n \over 1-q}\]
just different letters :) ...

Answer 4

oh okay :) thank you! so would it be 8(1-(19683) / -2

Answer 5

... quite close :)
it's:
\[\LARGE S_n=a_1\cdot {1-r^n \over 1-r}\]
\[\LARGE S_9=4\cdot {1-3^9 \over 1-3}\]
\[\LARGE S_9={4(1-19683) \over -2 }\]
Rembember
\[\LARGE a_1=4 \]
:)

Answer 6

would it be 39364? thats what i got? :)