PATTERNS, FUR1 2014 VCAA 1-2 MC

Paul went running every morning from Monday to Sunday for one week.
On Monday, Paul ran 1.0 km.
On Tuesday, Paul ran 1.5 km.
On Wednesday, Paul ran 2.0 km.
The number of kilometres that Paul ran each day continued to increase according to this pattern.

Part 1

The number of kilometres that Paul ran on Thursday is

A. `2.5`

B. `3.0`

C. `3.5`

D. `4.0`

E. `5.0`

Part 2

The total number of kilometres that Paul ran during the week is given by

A. the seventh term of an arithmetic sequence with `a = 1` and `d = 0.5`

B. the seventh term of a geometric sequence with `a = 1` and `r = 0.5`

C. the sum of seven terms of an arithmetic sequence with `a = 1` and `d = 0.5`

D. the sum of seven terms of a geometric sequence with `a = 1` and `r = 0.5`

E. the sum of seven terms of a Fibonacci-related sequence with `t_1 = 1` and `t_2 = 1.5`

Show Answers Only

`text(Part 1:)\ A`

`text(Part 2:)\ C`

Show Worked Solution

`text(Part 1)`

`text(Sequence is 1.0, 1.5, 2.0, …)`

`a = 1.0\ \ \ \ d = 1.5-1.0 = 0.5`

`T_4 = text(Thursday’s distance)`

`T_4`	`= a + (n-1) d`
	`=1.0 + (4-1) 0.5`
	`=2.5`

`=> A`

`text(Part 2)`

`text (Series is an arithmetic series with)\ a = 1.0 and d = 0.5`

`:.\ text(Total kms run in week is the sum of the first)`

`text(seven terms of the arithmetic series.)`

`=> C`