Mathematical Investigations III
Name ___
_
Sequences and Series
You may use a TI-30 Calculator on this exam. Justify all your work.
n
n
n(n  1)(2n  1)
n 2 (n  1) 2
2
3
Useful formulas:
j

j



6
4
j 1
j 1
True or False:
_____ 1. If Bert can mow the lawn in 2 hours and Ernie can mow it in three hours, then
it will take them 2.5 hours if they work together.
_____ 2. 0.2, 0.22, 0.222, 0.2222, 0.22222, . . . is a geometric sequence.
3. Consider the series:
4. Evaluate the series
8 4 2
  1
27 9 3
50
 (2n
3
. Write the series in
 n)
n 3
5. Write out the terms of the series,
5
  n  (n  2) .
n0
  notation.
 1
6a) Find  3   
2
k 1 
5

 1
b) Find  3   
2
k 6 
k 1
using the formula for a finite geometric series.
k 1
.
7. Find   2i 2  3 .
55
i 1
8. The fifth term in an arithmetic sequence is 9 and the 23rd term is 54. Find the sum of all 23
terms.
Sequences and Series Test MU
F 12
3
its height on each bounce.
4
a) State the formula for the height of the ball after the nth rebound.
9. A ball is dropped from a height of 20 feet and rebounds
b) Using

notation, state the total distance the ball travels assuming it bounces
?
indefinitely. (You may write your answer in the form 20   an
n ?
c) Find the total distance the ball travels.
10.
3

an   2
 3 an 1
if n  1
if n  1
a) State the first five terms of the sequence using common fractions.
b) Give an explicit formula for the sequence.
Sequences and Series Test MU
F 12