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
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 30, d = - 3 and [tex]a_{n}[/tex] = 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
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , thus
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] [ (2 × 30) + (9 × - 3 ) ]
= 5(60 - 27) = 5 × 33 = 165
There are 165 logs in the stack
