Math 2012 Quiz 3 Practice Spring 2008
Name: Last ____________________, First ____________________
You must show all work to get credit for the problems. NO work or explanations - no credit.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1)
At a plant that packages bottled spring water, the water is passed through a sequence of
ion-exchange filters to reduce the sodium content prior to bottling. Each filter removes 21% of the
sodium present in the water passing through it. Determine the number of filters that must be used
to reduce the sodium concentration from 21 parts-per-million to 0.96 parts-per-million.
A)
13
B)
12
C)
11
D)
10
1)
Write the first four elements of the sequence.
2)
1 +
1
n
n
A)
0, 1,
9
4,
64
27
B)
0, 2,
9
4,
64
27
C)
1,
9
4,
64
27 ,
625
64
D)
2,
9
4,
64
27 ,
625
256
2)
A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
3)
a1 = 1, an+1 =
n
a
n
n + 5
A)
1,
1
6,
7
6,
7
48 ,
63
480
B)
1,
1
6,
2
42 ,
3
336 ,
4
3024
C)
1,
1
6,
2
42 ,
6
336 ,
24
3024
D)
1,
1
6,
2
7,
6
8,
24
9
3)
Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
4)
8 -
8
3 +
8
9 -
8
27 + ... + (-1)n-1
8
3n-1 + ...
A)
8 1 -
1
(-3)n
1 + 1
3
; 12
B)
8 1 -
1
(-3)n
1 + 1
3
; 6
C)
8 1 -
1
(-3)n-1
1 + 1
3
; 12
D)
8 1 -
1
(-3)n-1
1 + 1
3
; 6
4)
Find the sum of the geometric series for those x for which the series converges.
5)
∞
n=0
(-1)n x - 9
7
n
∑
A)
7
2 + x
B)
7
2 - x
C)
7
-2 - x
D)
7
-2 + x
5)
1
