Logs in the lowest layer
Algebra
Level
2
A man piles 150 logs in layers so that the top layer contains 3 logs and each lower layer has one more log than the layer above. How many logs are in the lowest layer?
The answer is 17.
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1 solution
by Arithmetic Progressions
3,4,5,6 .....
S = n / 2 [ 2 a + ( n − 1 ) d ]
where:
S = sum of the progression
n = number of terms
a = first term
d = common difference
substitute:
1 5 0 = n / 2 [ 2 ∗ 3 + ( n − 1 ) 1 ]
3 0 0 = n ( 5 + n )
n 2 + 5 n − 3 0 0 = 0
n = 15
The number of logs in the lowest layer is the last term of the Arithmetic Progression.
L = a + (n-1)d
L = 3 + (15-1)1
L = 17