Question 39195: Still do not understand. Please help again.
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:
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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 7 significant figures.
Answer:
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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 7 significant figures.
Answer:
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d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
r is the number which is used to multiply a term of the sequence to
get the following term of the sequence. So to determine "r" you need
to divide any term of the sequence by the term immediately preceding it.
For example, divide the 2nd term by the 1st term to get the following:
r = [1/3]/1= 1/3
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 7 significant figures.
Answer:
Show work in this space.
The formula for the sum of "n" terms is as follows:
S(n)=a(1)[r^n-1]/[r-1]
a(1)=1 in your problem
So, the sum of the first 10 terms is as follows:
S(10)=1[r^10-1]/[r-1]= [(1/3)^10-1]/[1/3 - 1]
=-0.99998306.../(-2/3)1.49997460...
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 7 significant figures.
Answer:
Show work in this space.
Similarly the sum of the first 12 terms is as follows:
S(12)=1[(1/3)^12 - 1]/[(1/3)-1]= -0.99999812.../(-2/3)
=1.49999718...
d) What observation can you make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
As you take more and more terms the sum of the sequence of terms
gets closer and closer to 1.5
Cheers,
Stan H.
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