Question 39455: Please help.
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?
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.
Divide any term by the term preceding it to find "r".
For example r=9/3=3
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: The nth term is a(n)=a(1)r^(n-1) where a(1) is the 1st term.
a(10)=a(1)r^(10-1)
a(10)=(1)3^9=19683
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.
The sum of n terms is S(n)=a(1)[(r^(n)-1)/(r-1)]
a(1) means the 1st term.
So, S(10)=(1)[3^(10)-1)/(3-1)]=[(59049-1)/2]=29524
Cheers,
Stan H.
|
|
|
