SOLUTION: 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.

Algebra ->  Sequences-and-series -> SOLUTION: 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.       Log On


   

Question 87237: 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) About Me  (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:
r=27%2F9=3 Divide the term of 27 by 9
So the ratio is
r=3

b)
The sequence is multiplying by a factor of 3 each term, so the sequence is 3%5En
This means the 10th term is
3%5E9=19683(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
S=a%281-r%5En%29%2F%281-r%29where a=1
S=%281-3%5E10%29%2F%281-3%29 Plug in r=3 and n=10
S=%281-59049%29%2F%28-2%29 Evaluate 3%5E10
S=%28-59048%29%2F%28-2%29 Subtract
S=29524 Divide
So the sum of the first ten terms is 29,524