A pile of wood has 13 logs in the bottom row, 11 logs in the next bottom row, and so on, with two less logs in each row until the top row which consists of 1 log How many logs are there in the pile?
Add an Answer
More Questions From This User See All
Answers & Comments
Answer:
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(1303) (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?
======================
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
Step-by-step explanation:
sana maka tulong
Answer:
tama po yung sagot sa itaas