SOLUTION: 1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b)Usin
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Question 33818This question is from textbook College Algebra
: 1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space
d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space
e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
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
3)Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…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 sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
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? Please round your answer to 4 decimals.
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:
This question is from textbook College Algebra
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE ANSWERS BELOW
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1)Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer: 2
Show work in this space.
3-1=5-3=...ETC...=2
b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: T101=1+100*2=201
Show work in this space.
TN=A+(N-1)D....A=1....N=101......D=2
c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer: S20=(20/2){2*1+(20-1)2}=10*40=400
Show work in this space
SN=(N/2){2A+(N-1)D}
d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer: S30=15*60=900
Show work in this space
SAME AS ABOVE
e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer: SN=N^2
SN=(N/2){2+(N-1)2}=N*2N/2=N^2
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: 2
Show work in this space.
2/1=4/2=8/4=....ETC...=2
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
Answer: T24=1*{2^23)=2^23
Show work in this space.
TN=A*R^(N-1)
c)Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer: S10=1*{2^10-1}
Show work in this space
SN=A*{R^N-1}/(R-1)....N=10...R=2....A=1
3)Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a)What is r, the ratio between 2 consecutive terms?
Answer: 1/2
Show work in this space.
(1/2)/1=(1/4)/(1/2)=...ETC...1/2
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? Please round your answer to 4 decimals.
Answer: {1-(1/2)^10}/(1-1/2)
Show work in this space.
SN=A{1-R^N}/(R-1)
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? Please round your answer to 4 decimals.
Answer: {1-(1/2)^12}/(1-1/2)
Show work in this space.
SAME AS ABOVE
d)What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
THE SUM APPROACHES 1/(1-1/2)=2 AS N INCREASE TO LARGE NUMBERS...
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