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Question 84945: IS anyone able to help me? Don't have any idea what do.
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?
b) Using the formula for the sum of the first n terms of a geometric sequence, 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 sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! IS anyone able to help me? Don't have any idea what do.
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?
To find "r" divide any term by the term in front of it.
Your Problem: 1/9 / 1/3 = 3/9 = 1/3
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b) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.
Formula: S(n) = a(1)[r^(n+1)-1]/[r-1]
Your Problem:
S(10) = 1 [(1/3)^11 - 1/[(1/3)-1]
= [-.999999]/[-2/3]
= 1.4999999
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c) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
S(12) = 1[(1/3)^13 - 1]/ [(1/3) - 1]
= -0.99999999 / (-2/3)
= 1.4999999999
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d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than?
Smaller than 1.5
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Cheers,
Stan H.
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