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PATTERNS, FUR1 2009 VCAA 9 MC

There are 10 checkpoints in a 4500 metre orienteering course.

Checkpoint 1 is the start and checkpoint 10 is the finish.

The distance between successive checkpoints increases by 50 metres as each checkpoint is passed.

The distance, in metres, between checkpoint 2 and checkpoint 3 is

A.   `225`

B.   `275`

C.   `300`

D.   `350`

E.   `400`

Show Answers Only

`D`

Show Worked Solution

`text(9 distances exist between 10 checkpoints)`

♦♦ Mean mark 26%.

`text(9 distances form an AP, where)`

`d = 50,\ \ \ S_9 = 4500`

`S_n` `= n/2[2a + (n − 1)d]`
`4500` `= 9/2 [2a + (9 − 1) × 50]`
`4500` `= 9/2[2a + 400]`
`9a` `= 2700`
`a` `= 300`

`:.\ text(Distance between checkpoint 1 and 2)`

`= a=300\ text(m)`

`:.\ text(Distance between checkpoint 2 and 3)`

`= a+d=350\ text(m)`

`=>  D`