SOLUTION: write arithmetic series 17+21+25+......+417 in summation notation

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Question 699388: write arithmetic series 17+21+25+......+417 in summation notation
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
The nth term of an arithmetic sequence is
a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d.
In the sequence, 17, 21, 25, ..., 417
a%5B1%5D+=+17+ and d = 4, therefore
a%5Bn%5D+=+17+%2B+%28n-1%29%284%29+ or
a%5Bn%5D+=+4n+%2B+13+
To determine the number of terms, we solve
4n + 13 = 417
n = 101
So 17+21+25+......+ 417 in summation notation is
highlight%28sum%28+%284n+%2B+13%29%2C+n+=+1%2C+101%29+%29