PATTERNS, FUR1 2011 VCAA 6 MC

For which one of the following geometric sequences is an infinite sum not able to be determined?

A. `4, 2, 1, 1 / 2\ . . .`

B. `1, 2, 4, 8\ . . .`

C. `–4, 2, –1, 1 / 2\ . . .`

D. `1, 1 / 2, 1 / 4, 1 / 8\ . . .`

E. `–1, 1/2, –1 / 4, 1 / 8\ . . .`

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`B`

Show Worked Solution

`text(An infinite sum can only be determined when)`

`|\ r\ | <= 1`

♦ Mean mark 50%.

`text(In A,)\ \ \ r = t_2 / t_1 = 1 / 2`

`text(In B,)\ \ \ r = 2 / 1 = 2`

`text(In C,)\ \ \ r = 2 / (–4) = – 1 / 2`

`text(In D,)\ \ \ r = 1 / 2`

`text(In E,)\ \ \ r = – 1 / 2`

`=> B`