SOLUTION: 2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space. b

Algebra ->  Sequences-and-series -> SOLUTION: 2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space. b      Log On


   

Question 74491: 2) Use the geometric sequence of numbers 1, 2, 4, 8,…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 24th term?
Answer:
Show work in this space.



c) Using the formula for the sum of a geometric series, 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!
The ratio r is the factor to get from term to term. So
r=nth term/(n-1) term
r=8%2F4=2
r=2
The sequence doubles each term, so the sequence is 2%5En
So the 24th term is
2%5E23=8388608(n=23 zero is the 1st term)
The sum of a geometric series is
S=a%281-r%5En%29%2F%281-r%29where a=1
S=%281-2%5E10%29%2F%281-2%29
S=%281-1024%29%2F%28-1%29
S=1023
So the sum of the first ten terms is 1,023