SOLUTION: 2) Use the geometric sequence of numbers 1, 3, 9, 27,
to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space
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Question 87197: 2) Use the geometric sequence of numbers 1, 3, 9, 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 nth term of a geometric sequence, what is the 10th term?
Answer:
Show work in this space.
c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
Answer:
Show work in this space.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
The ratio r is the factor to get from term to term. So to find r, simply pick any term and divide it by the previous term:
Divide the term of 27 by 9
So the ratio is
b)
The sequence is multiplying by a factor of 3 each term, so the sequence is
This means the 10th term is
(let n=9, remember n=0 is the 1st term)
So the 10th term is 19,683
c)
The sum of a geometric series is
where a=1
Plug in and
Evaluate
Subtract
Divide
So the sum of the first ten terms is 29,524
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