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PATTERNS, FUR1 2007 VCAA 9 MC

At the end of the first day of a volcanic eruption, 15 km2 of forest was destroyed.

At the end of the second day, an additional 13.5 km2 of forest was destroyed.

At the end of the third day, an additional 12.15 km2 of forest was destroyed.

The total area of the forest destroyed by the volcanic eruption continues to increase in this way.

In square kilometres, the total amount of forest destroyed by the volcanic eruption at the end of the fourteenth day is closest to

A.   `116`

B.   `119`

C.   `150`

D.   `179`

E.   `210`

Show Answers Only

`A`

Show Worked Solution

`15, 13.5, 12.15,\ …`

`text(GP where)\ \ \ a` `=15, and`
`r` `=t_2/t_1=13.5/15=0.9`
`S_n` `=(a(1-r^n))/(1-r)`
`:.S_14`

`=(15(1-0.9^14))/(1-0.9)`

  `=115.68…`

`rArr A`

Filed Under: APs and GPs - MC Tagged With: Band 5

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