PATTERNS, FUR1 2013 VCAA 7 MC

The following are either three consecutive terms of an arithmetic sequence or three consecutive terms of a geometric sequence.

Which one of these sequences could not include 2 as a term?

A. `–1, 0.5, –0.25`

B. `–1, –3, –5`

C. `5, 12.5, 31.25`

D. `6, 8, 10`

E. `8, 16, 32`

Show Answers Only

`B`

Show Worked Solution

`text(By elimination,)`

`text(In A, GP where)\ \ r=0.5/-1=-0.5`

`:.\ text(Term before −1 is 2.)`

`text(In B, AP where)\ \ d=-2`

`:.\ text{Terms before −1 = −1 − (−2) = 1}`

`text{Term before 1 = 1 − (−2) = 3}`

`:.\ text(Does NOT include 2.)`

`text(Other choices can all be shown to contain 2.`

`=> B`