Question 53667: Use the arithmetic sequence of numbers 1. 3, 5, 7, 9,...to find the following:
a) what is d, the differenc between any 2 terms?
b) Using the formula for the nth term of an arithmetic sequence, what is 101th term?
c) Using the formula for the sum of an arthmetic series, what is the sum of the first 20 terms?
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?
d=3-1=2
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b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
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?
S(n)=(1/2)n(a(1)+a(n))
S(20)=(1/2)(20)(1+a(20))
But a(20)=1+19(2)=39
So 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?
Use the formula I just used but let n=30.
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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."
I gave you the formula in part "c".
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Cheers,
Stan H.
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