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

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studentdiversified's profile pic

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

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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