SOLUTION: Still do not understand. Please help again.
3) 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
Algebra.Com
Question 39195: Still do not understand. Please help again.
3) 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?
Answer:
Show work in this space.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 7 significant figures.
Answer:
Show work in this space.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 7 significant figures.
Answer:
Show work in this space.
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
3) 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?
Answer:
Show work in this space.
r is the number which is used to multiply a term of the sequence to
get the following term of the sequence. So to determine "r" you need
to divide any term of the sequence by the term immediately preceding it.
For example, divide the 2nd term by the 1st term to get the following:
r = [1/3]/1= 1/3
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 7 significant figures.
Answer:
Show work in this space.
The formula for the sum of "n" terms is as follows:
S(n)=a(1)[r^n-1]/[r-1]
a(1)=1 in your problem
So, the sum of the first 10 terms is as follows:
S(10)=1[r^10-1]/[r-1]= [(1/3)^10-1]/[1/3 - 1]
=-0.99998306.../(-2/3)1.49997460...
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 7 significant figures.
Answer:
Show work in this space.
Similarly the sum of the first 12 terms is as follows:
S(12)=1[(1/3)^12 - 1]/[(1/3)-1]= -0.99999812.../(-2/3)
=1.49999718...
d) What observation can you make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
As you take more and more terms the sum of the sequence of terms
gets closer and closer to 1.5
Cheers,
Stan H.
RELATED QUESTIONS
Can anyone help me with this? I'm stuck again and don't understand this geometric... (answered by Edwin McCravy)
Any help here?
Use the geometric sequence of numbers 1, 3, 9, 27, … to find the... (answered by jim_thompson5910)
Please help again, appreciate any and all help.
2) Use the geometric sequence of numbers (answered by longjonsilver)
Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is... (answered by rmromero)
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a)... (answered by stanbon)
did I do this right: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the... (answered by fractalier)
Use the geometric sequence of numbers 1, 3, 9, 27 … to find the following:
a) What is... (answered by jim_thompson5910)
I am having trouble with this problem, could you please help me.
3) Use the geometric... (answered by sdmmadam@yahoo.com)
Hello I really need help. PLEASE HELP ME...
Use the geometric sequence of numbers... (answered by vertciel)