Question

A stack of logs has 17 logs on the bottom layer. Each subsequent layer has 3 fewer logs than the previous layer. If the top layer has two logs, how many total logs are in the pile?

Answer 1

Answer:

152 logs

Step-by-step explanation:

This question is an Arithmetic progression question

A stack of logs has 17 logs on the bottom layer.

First term = a1 = 17

We are told that: each subsequent layer has 3 fewer logs than the previous layer.

Common difference = 3

Hence, Second term = 17 - 3 = 14

Third term = 14 - 3 = 11

If the top layer has two logs,

Last term = 2

Step 1

We find the number of layers of logs present

Number of logs in the bottom layer - number of logs in the first layer + 1

= 17 - 2 +1

= 16 layers

Step 2

We are asked in the question to find , how many total logs are in the pile?

This means, we are to find the sum of terms in the Arithmetic progression.

The formula is given as

Sn = n/2(a + l)

Where a = First term = 17

l = Last term = 2

Sn = n/2(17 + 2)

Sn = 16/2(19)

Sn = 8 × 19

Sn= 152 logs