SOLUTION: A stack of wood has 44 pieces on the bottom row and 40 in top of those,then 36, and so on. If there are 260 pieces of firewood, how many rows are there in the stack?

Algebra ->  Sequences-and-series -> SOLUTION: A stack of wood has 44 pieces on the bottom row and 40 in top of those,then 36, and so on. If there are 260 pieces of firewood, how many rows are there in the stack?      Log On


   

Question 1023561: A stack of wood has 44 pieces on the bottom row and 40 in top of those,then 36, and so on. If there are 260 pieces of firewood, how many rows are there in the stack?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
General term, 44%2B%28-4%29%28n-1%29
44-4n%2B4
48-4n

Apply the summation formula for arithmetic progression
%2848%2B44-4n%29%28n%2F2%29=260

%2824%2B22-2n%29n=260
%2846-2n%29n=260
%2823-n%29n=130
-n%5E2%2B23n-130=0
n%5E2-23n%2B130=0

n=%2823%2B-+sqrt%2823%5E2-4%2A130%29%29%2F2
n=%2823%2B-+sqrt%289%29%29%2F2
n=%2823%2B-+3%29%2F2
n is either 10 or 13;
but they cannot both be correct.

CHECK WHICH n value:
10?
48-4n
48-4*10
8
Last row would have 8 pieces.
13?
48-4*13
48-52
-4
Last row would not be able to have NEGATIVE FOUR pieces.

Correct answer is n=10.