<PRE><B>Question 64676</B>
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 &quot;n.&quot;
Answer: The sums get larger and larger as n gets larger and larger.
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Cheers,
Stan H.

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