Honors Pre-Calculus & Trigonometry Name:_______________________________

Sequences & Series Test VERSION 2 Thursday, October 6, 2011

Instructions: Show work or provide an explanation for each problem. No work receives no credit. Good luck and have

fun-ctions!

(4 points) 1. In a game similar to the Towers of Hanoi, the minimum number of moves required for a specific number of

disks is shown in the table below. Write an explicit formula to determine the number of moves for n disks. Then, use

your formula to determine the minimum number of moves for 8 disks.

# of disks 1 2 3 4 5

Minimum number of moves

2 8 26 80 242

(2 points) 2. Write a recursive formula for 2, 5, 7, 12, 19,…..

(2 points) 3. What is the difference between an explicit formula & a recursive formula? Write no more than two

sentences.

(2 points) 4. Expand & simplify:

∑( )

(4 points) 5. Think about the copier problem. If you punch in 60% reduction and pass a rectangle through with an

original area of 150cm2, then the formula to find the area of the nth figure can be found with this equation:

( ) . If you copied at this reduction over and over (as in the video), what would be the SUM of the areas

of all of the rectangles?

(4 points) 6. In an arithmetic sequence a7 = 17 and a11 = 9. Find a20.

(4 points) 7. Find a1 in a geometric sequence where

and

. There may be more than one answer.

(4 points) 8. In an arithmetic series, find S22 if a1=7 and d = -2.

(6 points) 9. For an arithmetic series, find n if a1 = -3, d = 3, and Sn = 42.

(4 points) 10. Use the formula to find S5 in the geometric series with r = -2 and a1 = 3.

(2 points) 11. Evaluate (show work!)

(4 points) 12. Write -0.4545454545…… as a fraction in lowest terms.