What is the sum of the geometric sequence 1, 3, 9, if there are 12 terms? (5 points)

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

 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

* Lets solve the problem

∵ The geometric sequence is 1 , 3 , 9 , .............

∵

∴

∵ There are 12 terms

∴ n = 12

∵ The first term is 1

∴ a = 1

∴

* The sum of the 12 terms is 265720

69.64%

step-by-step explanation: