Question 64676: I am having problems with this. I think I have figured out the first one. Thanks in advance for any help.
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: d = 2
Show work in this space.
1 +2 =3 + 2 =5 + 2 = 7 etc.
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.)? Express your observations as a general formula in "n."
Answer:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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: d = 2
Show work in this space.
1 +2 =3 + 2 =5 + 2 = 7 etc.
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
a(n)=a(1)+(n-1)d
a(101)=1+100(2)
a(101)=201
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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
S(n)=(n/2)(a(1)+a(n))
s(20)=(20/2)(1+[1+19*2])
S(20)=10(40)=400
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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
S(30)=(30/2)(1+1+29*2)
S(30)=15(60)=900
Cheers,
Stan H.
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.)? Express your observations as a general formula in "n."
Answer: The sums get larger and larger as n gets larger and larger.
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Cheers,
Stan H.
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