PATTERNS, FUR1 2009 VCAA 5 MC

On Monday morning, Jim told six friends a secret. On Tuesday morning, those six friends each told the secret to six other friends who did not know it. The secret continued to spread in this way on Wednesday, Thursday and Friday mornings.

The total number of people (not counting Jim) who will know the secret on Friday afternoon is

A. `259`

B. `1296`

C. `1555`

D. `7776`

E. `9330`

Show Answers Only

`E`

Show Worked Solution

`text(Sequence is 6, 6 × 6, 6 × 6 × 6, …)`

♦♦ Mean mark 25%.
MARKERS’ COMMENT: Over 50% of students calculated the 5th term and not the sum of the first 5 terms!

`text(GP where)\ \ \ a`	`= 6, and`
`r`	`= 6 `

`S_n=`	`text(total number who know the secret)`
	`text(on the afternoon of day)\ n`

`text(On Friday,)\ \ n = 5`

`S_n`	`= (a (r^n − 1)) / (r −1)`
`:.S_5`	`= (6(6^5 −1)) / (6 −1)`
	`= 9330`

`=> E`