SOLUTION: What is the sum of a 6-term geometric series if the first term is 19 and the last term is 319,333?

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Question 773412: What is the sum of a 6-term geometric series if the first term is 19 and the last term is 319,333?
Found 2 solutions by MathTherapy, KMST:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the sum of a 6-term geometric series if the first term is 19 and the last term is 319,333?

highlight_green%28S%5B6%5D+=+372552%29

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a geometric sequence the ratio of consecutive terms equals a number r, called the common ratio.
The nth term of a geometric sequence is given by
b%5Bn%5D=b%5B1%5D%2Ar%5E%28n-1%29 where
b%5B1%5D is the first term, and
r is the common ratio
The sum of the first n terms is S%5Bn%5D=b%5B1%5D%2A%28r%5En-1%29%2F%28r-1%29

In your case,
b%5B1%5D=19
b%5B6%5D=19%2Ar%5E%286-1%29=19%2Ar%5E5=319333

19%2Ar%5E5=319333 --> r%5E5=319333%2F19 --> r%5E5=16087 --> r=root%285%2C16087%29 --> r=7

S%5B6%5D=19%2A%287%5E6-1%29%2F%287-1%29 --> S%5B6%5D=19%2A%28117649-1%29%2F6 --> S%5B6%5D=19%2A117648%2F6 --> highlight%28S%5B6%5D=372552%29