SOLUTION: 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27� to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space.

Question 69157: 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27� to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.

b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.

d) What observation can make about the successive partial sums of this series? In particular, what whole number does it appear that the sum will always be smaller than?
Answer:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
The ratio r is the factor needed to go from term to term. To find the factor, divide any term by its previous term. So I chose 1/3 as the first term to be divided by 1
Ratio r: pick any nth term and any previous term, such as the 2nd and 1st term.
I can also do it with 1/27 and 1/9 and it will still give me the same value

So r=1/3
b) The sum of the first ten terms can be found by using

So let r=1/3

c) Use the same technique but with 12 terms

let r=1/3

If it seems this sum is approaching 1.5 it is. If you go to the millionth term it will be even closer to 1.5
d)Using what we found from the two previous problems we can see that the partial sums, the pieces that make up the whole sum, are smaller than its previous term. This allows the entire series to approach 1.5

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