PATTERNS, FUR1 2013 VCAA 9 MC

Eleven speed bumps are placed on a road.

The speed bumps are placed so that the distance between consecutive speed bumps decreases according to an arithmetic sequence.

The distance between the first and last speed bumps is exactly 100 m.

The smallest distance between consecutive speed bumps is 2 m.

The largest distance, in m, between two consecutive speed bumps is

A. `16`

B. `18`

C. `20`

D. `22`

E. `24`

Show Answers Only

`B`

Show Worked Solution

`text(11 speed bumps over 100m distance has 10 intervals,)`

`text(so the series can be written)`

♦♦ Mean mark 33%.
MARKER’S COMMENT: The not often used formula `S_n=n/2(a+l)` provides the most efficient route to this solution, although `S_n=n/2[2a+(n-1)d]` can also be used after finding the value of `d`.

`a, a+d, a+2d, …, a+9d`

`text(Last distance)\ =a+9d=l=2\quad text{(given)}`

`S_10=100\ text(m)\ \ \ text{(given)}`

`text(Using)\ \ \ S_n`	`=n/2(a+l)`
`100`	`=10/2(a+2)`
`100`	`=5a+10`
`5a`	`=90`
`a`	`=18`

`:. 18text{m is largest distance (d is negative)}`

`=> B`