Question 53667
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.