Problema Solution
A pile of logs has 25 logs in the bottom layer, 24 in the second layer, 23 in the third, and so on. The top layer contains 11 logs. Find the total number of logs in the pile
Answer provided by our tutors
bottom layer has a1 = 25
second layer has a2 = a1 - 1 = 24
third layer has a3 = a2 - 1 = a1 - 2 = 23
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n-th layer has an an = a1 - n = 25 - n
the top layer contains an = 25 - n and we know that the top layer has 11 logs thus
25 - n = 11
n = 25 - 11
n = 14
there are 14 layers
the total number of logs is the sum of the first 14 members of the Arithmetic Progression 25, 24, 23, 23,.....11 where
an = 25 - n
Sn = (n/2)(a1 + an) and since n = 14
S14 = (14/2)(25 + 11) = 7*36 = 252
S14 = 252 logs
there are 252 logs in the pile.