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Arithmetic Sequences  Problem 1
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Finding a specific term in an arithmetic sequence so what we have behind me is a sequence we are given the first three terms and what we are trying to do is find the 301st term in the sequence. So we have options you could either write it in all out which I probably wouldn’t recommend because you are going to be writing for quite a while or we could use the general term for a arithmetic sequence, which hopefully you remember is a of n is equal to a1 to first term plus n minus 1 times d.
So we are looking for a301 and that is going to be equal to a1 which is just the first term which is just the first term, to 11, plus n minus 1 n is the term number that we are looking for, so our term number that we are looking for is 301 minus 1 and times d. And d is the difference, the common difference that we get from each term.
Basically what we need to do is figure out what we do to one term to get the next. The relationship between 11 and 7, we subtract 4 from 7 and 3 again subtract 4, so that’s our difference is 4.
We now have a pretty easy expression in order to solve for a 301 is just going to be equal to 11 plus 300 times 4, 11 plus 1200 simplifying this up and we get a301 is equal to 1189 and make sure I remember my negative sign.
So we are given a arithmetic sequence we know this because we are subtracting the exact thing every single time and using our general term for an arithmetic sequence so we are able to plug in what we know in order to find a of that term number.
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Carl Horowitz
B.S. in Mathematics University of Michigan
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Sample Problems (19)
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Arithmetic Sequences
Problem 1 11,054 viewsGiven 11, 7, 3...
Find a_{301}. 
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Problem 2 8,443 viewsGiven a_{20} = 101 and a_{21} = 104,
find the general term, a_{n}. 
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Problem 3 7,818 viewsGiven a_{11} = 52, a_{19} = 92,
find a_{1001} 
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Problem 4 7,277 viewsFind the number of terms:
7 , 13 , 19 ... 85 3 3 3 3 
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Problem 5 1,218 views 
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Problem 6 1,304 views 
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Problem 7 1,062 views 
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Problem 8 1,369 views 
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Problem 9 941 views 
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Problem 10 867 views 
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Problem 11 972 views 
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Problem 12 875 views 
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Problem 13 831 views 
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Problem 14 852 views 
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Problem 15 838 views 
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Problem 16 871 views 
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Problem 17 846 views 
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Problem 18 815 views 
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Problem 19 818 views
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