**Answer:**

see explanation

**Step-by-step explanation:**

The sequence of logs is

30, 27, 24, 21 .....

There is a common difference between consecutive terms in the sequence

d = 27 - 30 = 24 - 27 = 21 - 24 = - 3

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 30, d = - 3 and = 3 ( the last term ), thus

30 - 3(n - 1) = 3 ( subtract 30 from both sides )

- 3(n - 1) = - 27 ( divide both sides by - 3 )

n - 1 = 9 ( add 1 to both sides )

n = 10 ← number of layers in the stack

(b)

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ] , thus

= [ (2 × 30) + (9 × - 3 ) ]

= 5(60 - 27) = 5 × 33 = 165

There are 165 logs in the stack