Question

A stack of logs has 27 logs on the bottom layer each subsequent layer has five fewer logs in the previous layer at the top layer has to logs how many total Boggs are thereal

Answer 1

Answer:

S=252logs

Step-by-step explanation:

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