PATTERNS, FUR1 2014 VCAA 5 MC

Mary plans to read a book in seven days.
Each day, Mary plans to read 15 pages more than she read on the previous day.
The book contains 1155 pages.
The number of pages that Mary will need to read on the first day, if she is to finish reading the book in seven days, is

A. `112`

B. `120`

C. `150`

D. `165`

E. `180`

Show Answers Only

`B`

Show Worked Solution

`text(Sequence is)\ \ a, a+15, a + 2 xx 15, …`

`=>\ text(AP where)\ \ \d=15`

`text(Find)\ \ a\ \ text(when)\ S_7 = 1155`

`S_n`	`=n/2[2a + (n-1)d]`
`1155`	`=7/2[2a + (7-1)15]`
`1155`	`=7/2[2a + 90]`
	`=7a + 315`
`7a`	`=840`
`a`	`=120`

`=> B`