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

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studentdiversified's profile pic

studentdiversified | Student | (Level 3) Honors

Posted on

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

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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