Question 73025: (1)use the arithmatic sequence of numbers 1,3,5,7,9,...to find the following:
a)what is d,the difference between any two terms?
answer:
show work:
b)using the formula for the nth term of an arithmetic sequence, what is the 101st term?
answer:
show work:
c) using the formula for the sum of an arithmeitc sequence, what is the sum of the first 20 terms?
answer:
show work:
d)using the formula for the sum of an arithmetic sequence, wht is the sum of the first 30 terms?
answer:
show work:
e)what observaton can you make about these sums of this sequence? express your observations as a general formula in "n".
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (1)use the arithmatic sequence of numbers 1,3,5,7,9,...to find the following:
a)what is d,the difference between any two terms?
answer: 3-1=2 or 5-3=2: the common difference is "2"
show work:
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b)using the formula for the nth term of an arithmetic sequence, what is the 101st term?
answer: a(101)= a(1)+(100)(2) = 1+200 = 201
show work: a(n)=a(1)+(n-1)d
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c) using the formula for the sum of an arithmeitc sequence, what is the sum of the first 20 terms?
answer
S(n)=(n/2)(a(1)+a(n))
S(20) = 10(1+a(20))
But a(20)=1+19*2=39
So, S(20)=10(1+39)=400
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d)using the formula for the sum of an arithmetic sequence, wht is the sum of the first 30 terms?
answer:
S(30)=15(1+a(30))
But a(30)=1+29*2=59
So S(30)=15*60=900
show work:
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e)what observaton can you make about these sums of this sequence? express your observations as a general formula in "n".
As n gets larger S(n) gets larger.
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Cheers,
Stan H>
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