Answer:
The sum of the given geometric series if there are 12 terms is:
265,720
Step-by-step explanation:
We are given a geometric sequence as:
1,3,9,.....
This means that the common ratio(r) of the sequence is: 3
Since each term is increasing by a multiple of '3'
Also, sum of an finite geometric series with n terms is given by:
[tex]S_n=a\times (\dfrac{r^n-1}{r-1})[/tex]
where n is the number of terms whose sum is calculated and a is the first term of the sequence.
We have n=12, a=1 and r=3
Hence, the sum is:
[tex]S_{12}=1\times (\dfrac{3^{12}-1}{3-1})\\\\\\S_{12}=\dfrac{531440}{2}\\\\\\S_{12}=265720[/tex]
Hence, the sum is: 265,720
