PATTERNS, FUR1 2010 VCAA 3 MC

The prizes in a lottery form the terms of a geometric sequence with a common ratio of 0.95.
If the first prize is $20 000, the value of the eighth prize will be closest to

A. `$7000`

B. `$8000`

C. `$12\ 000`

D. `$13\ 000`

E. `$14\ 000`

Show Answers Only

`E`

Show Worked Solution

`text(GP has)\ \ r = 0.95`

`T_1`	`=a=20000`
`T_2`	`=ar=20000(0.95)=19\ 000`
`T_3`	`=ar^2=20000(0.95)^2=18\ 050`
`vdots`
`T_8`	`=ar^7=20000(0.95)^7=13\ 966.74`

`=> E`