Chapter 11: Further Topics in Algebra
11.1:
Sequences and Ser
ies
1.
.
The first five terms of the sequence are
2.
.
The first five terms of the sequence are
3.
.
The first five terms of the sequence are
4.
.
The first five terms of the sequence are
5.
The first five terms of the sequence are
6.
The first five terms of the sequence are
7.
The first five terms of the sequence are
8.
The first five terms of the sequence are
9.
The first five terms of the sequence are
10.
The first five terms of the sequence are
11.
The terms of a sequence are numbered according to their position in the sequence;
is the first term,
is the
second term, etc.
So
will be the
n
th
term in the sequence for any positive integer value of
n
.
12.
A sequence is a function which is defined on the positive integers.
That is, the positive integers are the domain
of the function and the terms of the sequence constitute the range of the function.
13.
The sequence has 7 terms; it is finite.
14.
The sequence has 30 terms; it is finite.
15.
The sequence has 4 terms; it is finite.
a
n
a
2
a
1
0,
3
5
,
4
5
,
15
17
,
12
13
.
a
5
5
2
1
5
2
1
24
26
12
13
.
a
4
4
2
1
4
2
1
15
17
;
a
3
3
2
1
3
2
1
8
10
4
5
;
a
2
2
2
1
2
2
1
3
5
;
a
1
1
2
1
1
2
1
0
2
2;
1,
7
6
, 1,
5
6
,
19
27
.
a
5
4
1
5
2
1
5
2
2
19
27
.
a
4
4
1
4
2
1
4
2
2
15
18
5
6
;
a
3
4
1
3
2
1
3
2
2
11
11
1;
a
2
4
1
2
2
1
2
2
2
7
6
;
a
1
4
1
1
2
1
1
2
2
3
3
1;
2, 3, 4, 5, 6.
a
5
1
1
2
5
1
1
5
1
2
1
1
2
4
1
6
2
6.
a
4
1
1
2
4
1
1
4
1
2
1
1
2
3
1
5
2
5;
a
3
1
1
2
3
1
1
3
1
2
1
1
2
2
1
4
2
4;
a
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
3
2
3;
a
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
2
2;
2, 4,
6, 8, 10.
a
5
1
1
2
5
3 1
2
21
5
2 4
10.
a
4
1
1
2
4
3 1
2
21
4
2 4
8;
a
3
1
1
2
3
3 1
2
21
3
2 4
6;
a
1
1
1
2
2
3 1
2
21
2
2 4
4;
a
1
1
1
2
1
3 1
2
21
1
2 4
2;
2, 8, 24, 64, 160.
a
5
1
2
2
5
1
5
2
160.
a
4
1
2
2
4
1
4
2
64;
a
3
1
2
2
3
1
3
2
24;
a
2
1
2
2
2
1
2
2
8;
a
1
1
2
2
1
1
1
2
2;
0,
1
9
,
2
27
,
1
27
,
4
243
.
a
5
a
1
3
b
5
1
5
1
2
a
1
243
b
1
4
2
4
243
.
a
4
a
1
3
b
4
1
4
1
2
a
1
81
b
1
3
2
1
27
;
a
1
a
1
3
b
3
1
3
1
2
a
1
27
b
1
2
2
2
27
;
a
2
a
1
3
b
2
1
2
1
2
a
1
9
b
1
1
2
1
9
;
a
1
a
1
3
b
1
1
1
1
2
a
1
3
b
1
0
2
0;
3,
9, 27, 81, 243.
a
5
3
5
243
a
4
3
4
81;
a
3
3
3
27;
a
2
3
2
9;
a
1
3
1
3;
1, 2, 4, 8, 16.
a
5
2
5
1
2
4
16
a
4
2
4
1
2
3
8;
a
3
2
3
1
2
2
4;
a
2
2
2
1
2
1
2;
a
1
2
1
1
2
0
1;
3, 9, 15, 21, 27.
a
5
6
1
5
2
3
27
a
4
6
1
4
2
3
21;
a
3
6
1
3
2
3
15;
a
2
6
1
2
2
3
9;
a
1
6
1
1
2
3
3;
14, 18, 22, 26, 30.
a
5
4
1
5
2
10
30
a
4
4
1
4
2
10
26;
a
3
4
1
3
2
10
22;
a
2
4
1
2
2
10
18;
a
1
4
1
1
2
10
14;
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16.
The sequence has 4 terms; it is finite.
17.
The sequence has no last term; it is infinite.
18.
The sequence has no last term; it is infinite.
19.
The sequence is defined for integer values of
n
from 1 through 10; it is finite.
20.
The sequence is defined for all positive integer values of
n
; it is infinite.
21.
The first four terms of the sequence are
22.
The first four terms of the sequence are
23.
The first four terms of the sequence are
24.
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 Spring '08
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 Calculus, Algebra, Sequences And Series, Geometric progression

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