SOLUTION: What is the sum of all integral multiples of 3 between 7 and 829?

Question 664290: What is the sum of all integral multiples of 3 between 7 and 829?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
What is the sum of all integral multiples of 3 between 7 and 829?
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This is an arithmetic series with the first term a1 = 9, and common difference of 3.
The highest integer multiple of 3 less than or equal to 829 is 828
The n-th term of an arithmetic series = a(n) = a1 + (n-1)d, where d is the common difference
So the formula for the series is a(n) = 9 + (n-1)*3 = 6 + 3n
The last term = 828
For the last term n = (828 - 6)/3 = 274
The sum of an arithmetic series = S(n) = (n/2)(a1+a(n)) = (274/2)(9+828) = 114669
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