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PATTERNS, FUR1 2012 VCAA 5 MC

On the first day of a fundraising program, three boys had their heads shaved. 

On the second day, each of those three boys shaved the heads of three other boys. 

On the third day, each of the boys who was shaved on the second day shaved the heads of three other boys.

The head-shaving continued in this pattern for seven days. 

The total number of boys who had their heads shaved in this fundraising activity was 

A.   `2187`

B.   `2188` 

C.   `3279`

D.   `6558`

E.   `6561`

Show Answers Only

`C`

Show Worked Solution

`text (Sequence is 3, 9, 27, …)`

♦ Mean mark 48%.
 `text (GP where)\ \ \  a` `= 3, and` 
 `r` `= t_2/t_1 = 9/3 = 3` 
 `S_7` `=\ text (Total boys with head shaved)` 
`S_n` `= (a (r^n – 1))/(r-1)`
`:. S_7` `= (3 (3^7 – 1))/(3-1)`
  `= 3279`

`rArr C`

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

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