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PATTERNS, FUR1 2012 VCAA 7 MC

A dragster is travelling at a speed of 100 km/h.

It increases its speed by

  • 50 km/h in the 1st second
  • 30 km/h in the 2nd second
  • 18 km/h in the 3rd second

and so on in this pattern.

Correct to the nearest whole number, the greatest speed, in km/h, that the dragster will reach is

A.   `125`

B.   `200`

C.   `220`

D.   `225`

E.   `250`

Show Answers Only

`D`

Show Worked Solution

`text (Sequence of speed increases is)`

`text (50, 30, 18, …)`

`text (GP where)\ \ \ a`  `= 50, and` 
`r` `= t_2/t_1 = 30/50 = 0.6`

 

`text (S) text (ince)\ \ |\ r\ | < |,`

`S_oo` `= a / (1-r)`
  `= 50/ (1 – 0.6)`
  `= 125`

`:.\ text (Max speed is 100 + 125 = 225 km/h)`

`rArr D`