SOLUTION: IN A PILE OF LOGS, EACH LAYER CONTAINS ONE MORE LOG THAN THE LAYER ABOVE,IN THE TOP LAYER CONTAINS JUST ONE LOG. IF THERE ARE 105 LOGS IN THE PILE, HOW MANY LAYERS ARE THERE?

Question 571989: IN A PILE OF LOGS, EACH LAYER CONTAINS ONE MORE LOG THAN THE LAYER ABOVE,IN THE TOP LAYER CONTAINS JUST ONE LOG. IF THERE ARE 105 LOGS IN THE PILE, HOW MANY LAYERS ARE THERE?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
IN A PILE OF LOGS, EACH LAYER CONTAINS ONE MORE LOG THAN THE LAYER ABOVE,IN THE TOP LAYER CONTAINS JUST ONE LOG. IF THERE ARE 105 LOGS IN THE PILE, HOW MANY LAYERS ARE THERE?
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This is an arithmetic sequence: 1,2,3,4... [counting down from the top of the pile]
The nth term of an arithmetic sequence is
a(n) = a(1) + (n-1)d where a(1) = the 1st term, d = the common difference
In this case a(n) = 1 + (n-1) = n
The sum of the 1st n terms of the sequence is S(n) = (n/2)(a(1) + a(n)) = 105
So S(n) = (n/2)(1+n) = 105
Solve for n:
n^2 + n - 210 = 0
Factor:
(n-14)(n+15) = 0
Take the positive solution, n=14
So there are 14 layers

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