SOLUTION: Is this correct? Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,�to find the following: What is r, the ratio between 2 consecutive terms? Answer: r = (1/2)/1 = 1/2

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Question 83996: Is this correct?
Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,�to find the following:
What is r, the ratio between 2 consecutive terms?
Answer: r = (1/2)/1 = 1/2
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Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
Answer:
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S(n) = a(1)[r ^(n + 1) � 1)/(r � 1)
S(10) = 1[(1/2) ^ 9 � 1] / [(1/2)-1]
S(10) = [-0.998046875�] / [-0.5] = 1.99609375�
Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
Answer:
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S(n) = a(1)[r ^(n + 1) � 1)/(r � 1)
S(12) = 1[(1/2) ^ 9 � 1] / [(1/2)-1]
S(12) = [-0.998046875�] / [-0.5] = 1.99609375�
n = 12

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

The ratio r is the factor to get from term to term. So
r=nth term/(n-1) term

The sequence is cut in half each term, so the sequence is

The sum of a geometric series is
where a=1
So plug in n=10 to find the sum of the first 10 partial sums

So the sum of the first ten terms is or 1.99805 approximately

Use the same formula to find the sum of the 1st 12 terms
where a=1
So plug in n=12 to find the sum of the first 12 partial sums

So the sum of the first twelve terms is or 1.99951 approximately