PATTERNS, FUR1 2011 VCAA 4 MC

The number of bees in a colony was recorded for three months and the results are displayed in the table below.

If this pattern of increase continues, which one of the following statements is not true.

A. There will be nine times as many bees in the colony in month 5 than in month 3.

B. In month 4, the number of bees will equal 270.

C. In month 6, the number of bees will equal 7290.

D. In month 8, the number of bees will exceed 20 000.

E. In month 10, the number of bees will be under 200 000.

Show Answers Only

`C`

Show Worked Solution

`text(Sequence is 10, 30, 90, …)`

`text(GP where)\ \ \ a`	` = 10, and`
`r`	` = t_2/t_1=30 / 10 = 3`

`text(In A,)\ \ T_5 = 10 xx 3^4 and T_3 = 10 xx 3^2`

`:. T_5 = T_3 xx 3^2\ \ text{(True)}`

`text(In B,)\ \ T_4 = 10 xx 3^3 = 270\ \ text{(True)}`

`text(In C,)\ \ T_6 = 10 xx 3^5 = 2430\ \ text{(NOT true)}`

`text(In D,)\ \ T_8 = 10 xx 3^7 = 21\ 870\ \ text{(True)}`

`text(In E,)\ \ T_10 = 10 xx 3^9 = 196\ 830\ \ text{(True)}`

`=> C`