PATTERNS, FUR1 2008 VCAA 5 MC

The first term of a geometric sequence is 9.

The third term of this sequence is 121.

The second term of this sequence could be

A. `– 65`

B. `– 33`

C. `56`

D. `65`

E. `112`

Show Answers Only

`B`

Show Worked Solution

`text(GP where) \ \ \ T_1=9, and T_3=121`

`T_1`	`=a=9`
`T_3`	`=ar^2=121`
`:.9r^2`	`=121`
`r^2`	`=121/9`
`r`	`= +-11/3`

`text(If)\ \ r=11/3,`

`T_2=ar=9 xx 11/3 = 33`

`text(If)\ \ r= – 11/3,`

`T_2=9 xx – 11/3 = – 33`

`=>B`