smc-714-70-RR and graphs

CORE*, FUR1 2006 VCAA 7 MC

The values of the first five terms of a sequence are plotted on the graph shown below.

The first order difference equation that could describe the sequence is

A. `t_(n+1) = t_n + 5,`	`\ \ \ \ \ t_1 = 4`
B. `t_(n+1) = 2t_n + 1,`	`\ \ \ \ \ t_1 = 4`
C. `t_(n+1) = t_n - 3,`	`\ \ \ \ \ t_1 = 4`
D. `t_(n+1) = t_n + 3,`	`\ \ \ \ \ t_1 = 4`
E. `t_(n+1) = 3t_n,`	`\ \ \ \ \ t_1 = 4`

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`B`

Show Worked Solution

`text(By elimination,)`

`text(There is no common difference between terms,)`

`:.\ text(Cannot be A, C or D.)`

`text(The equation in B has)\ \ t_2=9,\ \ text(while the equation)`

`text(in C has)\ \ t_2=12.`

`rArr B`

CORE*, FUR1 2011 VCAA 3 MC

The graph above shows the first five terms of a sequence.

Let `A_n` be the `n`th term of the sequence.

A difference equation that generates the terms of this sequence is

A. `A_(n+1) = 2A_n - 2`	`\ \ \ \ text(where) \ \ \ \ `	`A_1 =8`
B. `A_(n+1) = 3A_n`	`\ \ \ \ text(where) \ \ \ \ `	`A_1 =8`
C. `A_(n+1) = -2A_n`	`\ \ \ \ text(where) \ \ \ \ \ \ \ \ `	`A_1 =8`
D. `A_(n+1) = -1 / 2 A_n`	`\ \ \ \ text(where) \ \ \ \ `	`A_1 =8`
E. `A_(n+1) = -A_n - 1`	`\ \ \ \ text(where) \ \ \ \ `	`A_1 =8`

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`D`

Show Worked Solution

`A_1 = 8, \ \ A_2 = –4, \ \ A_3 = 2\ \ text{(from graph)}`

`text(This sequence is geometric where)`

`r=t_2/t_1=- 1/2`

`:.\ text(Difference equation is)\ \ \ A_(n+1) = -1/2 A_n`

`=> D`