Question 26238: I am very frustrated. I am working on geometric series of numbers and thought that it would be easy but, I have not done this in a while and I have to admit that I am perplexed. Here is what I must solve:
Use the geometric series of numbers 1, 2, 4, 8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
(I got r=1)
b) Using the formula for the nth term of a geometric series, what it the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Could you please help refresh my memory by showing me step by step how to complete this first set of problems? Thank you!!!!
Found 2 solutions by stanbon, AnlytcPhil:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! r=2/1 or 4/2 or 8/4; at any rate r=2
Formula for nth term: nth term=(1st term)(r^(n-1))
24th term=(1)(2^(23))=8388608
Formula for sum: Sum of n terms =(1st term)[1-r^n]/[1-r]
Sum of 10 terms =1[1-2^10]/[1-2]
= -1023/(-1)=1023
Cheers,
Stan H.
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website! I am very frustrated. I am working on geometric series of numbers and thought
that it would be easy but, I have not done this in a while and I have to admit
that I am perplexed. Here is what I must solve:
Use the geometric series of numbers 1, 2, 4, 8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
(I got r=1)
NO! First of all this is a SEQUENCE, not a SERIES. A SEQUENCE has commas
between its terms whereas a SERIES has plus signs between its terms.
There are three ways to find r for this geometric SEQUENCE. DIVIDE any term
by the previous term.
First way to get r:
Divide the 2nd term by the 1st term. That is, 2 divided by 1 gives 2. So r=2
Second way to get r:
Divide the 3rd term by the 2nd term. That is, 4 divided by 2 gives 2. So r=2.
Third way to get r:
Divide the 4th term by the 3rd term. That is, 8 divided by 4 gives 2. So r=2.
Now you know how to find the common ratio r. I think you used SUBTRACTION,
which is what you use with an ARITHMETIC sequence to find the common
difference d, not common ratio r. You are getting a GEOMETRIC sequence
confused with an ARITHMETIC sequence.
b) Using the formula for the nth term of a geometric series, what it the 24th
term?
Again the word is SEQUENCE, not SERIES. Use SEQUENCE when commas separate the
terms. Use SERIES when plus (or minus) signs separate the terms.
The formula for the nth term of a geometric sequence is
an = a1rn-1
Here a1 = first term = 1, n = 24, r = 2
a24 = (1)(2)24-1
a24 = 223 = 8388608
c) Using the formula for the sum of a geometric series, what is the sum of the
first 10 terms?
Now you are correctly asking about a SERIES 1 + 2 + 4 + 8 + ···
Sn = a1(rn-1)/(r-1)
n = 10, a1 = 1, r = 2
S10 = 1(210-1)/(2-1) = (210-1)/1 = 210-1 = 1024-1 = 1023
Edwin McCravy
AnlytcPhil@aol.com
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