For every positive integer n, the nth term of a sequence is the total sum of three consecutive ...
For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 100 of this series?
Answer/Solution
15,450
Steps/Work
Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 100, the sum of the series is:
3(1+2+...+100) + 100(3) =
3(100)(101)/2 + 100(3) =
150*101 + 300 = 15,450
The answer is E.
Since the series goes from 1 to 100, the sum of the series is:
3(1+2+...+100) + 100(3) =
3(100)(101)/2 + 100(3) =
150*101 + 300 = 15,450
The answer is E.