Answer:
The sum of the 12 terms is 265720
Step-by-step explanation:
* Lets revise the geometric sequence
- There is a constant ratio between each two consecutive terms in the
geometric sequence
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
- The rule of the general term in the sequence is [tex]a_{n}=ar^{n-1}[/tex]
where a is the first term , r is the common ratio between each two
consecutive terms and n is the position of the term
- The sum of first n terms of a geometric series is calculated from
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
* Lets solve the problem
∵ The geometric sequence is 1 , 3 , 9 , .............
∵ [tex]r=\frac{a_{2}}{a_{1}}[/tex]
∴ [tex]r=\frac{3}{1}=3[/tex]
∵ There are 12 terms
∴ n = 12
∵ The first term is 1
∴ a = 1
∴ [tex]S_{12}=\frac{1(1-3^{12})}{(1-3)}=265720[/tex]
* The sum of the 12 terms is 265720
