Question 83716
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive terms? 
Answer: 
Show work in this space
d is the difference between any term and its previous term
d=3-1 = 2
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b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: 
Show work in this space. 

nth term = a(n) = a(1)+(n-1)d
a(101) = 1 + 100*2 = 201
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c) Using the formula for the sum of an arithmetic sequence, 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 + a(20))

S(20) = 10(1+1+19*2)
S(20 = 10(40) = 400
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d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Answer: 
Show work in this space 
S(30) = 15(1+1+29*2)
S(30) = 15(60) = 900
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e) What observation can you make about these sums of this sequence (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 are obviously increasing.
I listed the formula.
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Cheers,
Stan H.