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? 
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.