Question 1102305
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Not clear; but I will make a guess as to what the question is supposed to be.<br>
The r-th term of the sequence is 21-3r, so the sequence is 18, 15, 12, ....<br>
You want to know how many terms there need to be in the sequence for the sum of the terms to be zero.<br>
The problem is probably easiest to solve informally, without using formal algebraic methods.<br>
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.<br>
After that, the terms are the same size but opposite signs of earlier terms.<br>
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.<br>
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.