Question

A timber merchant needs to transport logs of wood on a truck . The logs are arranged , Such that the base layer contains 20 logs , the layer above it ,19 . Each layer has 1 log Less than the layer below it , leaving the top most layer with a single log. Find the Number of layers thus formed and the total number of logs transported . it is an arithmetic progression word problem. pls give me a step by step explanation.

Answer 1

Given: The logs are arranged , Such that the base layer contains 20 logs , the layer above it ,19 . Each layer has 1 log Less than the layer below it.

To find: The Number of layers thus formed and the total number of logs transported.

Solution:

• Now we have given that base layer has 20 logs and each layer has 1 log Less than the layer below it.

• So the layers will be:

                         20, 19 , 18 , 17 , 16 ............................... , 1.

• The layers formed are 20.

• Now this is an Arithmetic progression with first term 20, common difference -1 and number of layers as 20 and last term is 1

• So the total rods will be:

                         S(n) = n/2 { a + l }

                                = 20/2 { 20 + 1 }

                                = 10(21)

                                = 210

• So the total rods are 210.

Answer:

               So the layers formed are 20 and the total rods are 210.