Homework Help

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

user profile pic

demadcrazy | Student, Grade 10 | eNoter

Posted August 8, 2011 at 3:26 PM via web

dislike 1 like

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

2 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted August 8, 2011 at 3:32 PM (Answer #1)

dislike 0 like

First, we'll determine the common ratio of the geometric sequence:

q = 12/4 = 36/12 = 3

Now, we'll apply the formula that gives the sum of n terms of a geometric sequence:

`S_(n)` = `b_(1)` * (`q^(n)` - 1)/(q - 1)

We know that the number of terms involved in the sum is 9 and the first term is `b_(1)` = 4:

`S_(9)` = 4*(`3^(9)` - 1)/(3-1)

`S_(9)` = 2*(3^9 - 1)

`S_(9)` = 39364

user profile pic

studentdiversified | Student | Honors

Posted August 8, 2011 at 3:35 PM (Answer #2)

dislike 0 like

You can see that

sequence is increasing by multiplying a number by 3. For example multiplying first number "4" by "3" will give you 12, then 12 times 3 will give you 36 and so on. Doing that will give you this sequence

4,12,36,108,324,972,2916,8748,26244

When you sum them up you will get 39364

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes