Question

15 ma

1) There is a stack of logs in the backyard of a certain house. If there are 30 logs in the 1" layer,
27 in the 2nd layer. 24 in the 3rd layer, 21 in the 4th layer and so on with the last having three
How many layers are on the stack.
[2 ma
How many logs are in the stack
12​

Answer 1

see explanation

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

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 30, d = - 3 and
`a_(n)` = 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

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ] , thus

`S_(10)` =
`(10)/(2)` [ (2 × 30) + (9 × - 3 ) ]

= 5(60 - 27) = 5 × 33 = 165

There are 165 logs in the stack