Question 1102305: the sum of the first nth term of the series where the r term is a 21-3r how many terms must be taken for the sum to be zero
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Not clear; but I will make a guess as to what the question is supposed to be.
The r-th term of the sequence is 21-3r, so the sequence is 18, 15, 12, ....
You want to know how many terms there need to be in the sequence for the sum of the terms to be zero.
The problem is probably easiest to solve informally, without using formal algebraic methods.
We are starting with 18 and subtracting 3 each time. 18/3 = 6, so after we subtract 3 6 times the term will be 0. So the 7th term of the sequence is 0.
After that, the terms are the same size but opposite signs of earlier terms.
For the sum of all the terms to be zero, we will have to have as many terms after the 7th term (0) as we had before the 7th term.
So we have the 7th term zero, with 6 (positive) terms before that and 6 (negative) terms after that; the total number of terms is 6+1+6 = 13.
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