8.1. SEQUENCES
449
Month Interest earned Total amount of money in the account
0
$0
$5000.00
1
$33.33
$5033.33
2
3
4
5
6
7
8
9
10
11
12
Table 8.1: Interest
(d) How many years will it be before the account has doubled in value to $10000?
⊲⊳
Sequences
As our discussion in the introduction and Preview Activity 8.1 illustrate, many discrete
phenomena can be represented as lists of numbers (like the amount of money in an account
over a period of months). We call these any such list a sequence. In other words, a sequence
is nothing more than list of terms in some order. To be able to refer to a sequence in a
general sense, we often list the entries of the sequence with subscripts,
s 1 , s 2 , . . . , s n . . . ,
where the subscript denotes the position of the entry in the sequence. More formally,
Definition 8.1. A sequence is a list of terms s 1 , s 2 , s 3 , . . . in a specified order.
As an alternative to Definition 8.1, we can also consider a sequence to be a function f
449
Month Interest earned Total amount of money in the account
0
$0
$5000.00
1
$33.33
$5033.33
2
3
4
5
6
7
8
9
10
11
12
Table 8.1: Interest
(d) How many years will it be before the account has doubled in value to $10000?
⊲⊳
Sequences
As our discussion in the introduction and Preview Activity 8.1 illustrate, many discrete
phenomena can be represented as lists of numbers (like the amount of money in an account
over a period of months). We call these any such list a sequence. In other words, a sequence
is nothing more than list of terms in some order. To be able to refer to a sequence in a
general sense, we often list the entries of the sequence with subscripts,
s 1 , s 2 , . . . , s n . . . ,
where the subscript denotes the position of the entry in the sequence. More formally,
Definition 8.1. A sequence is a list of terms s 1 , s 2 , s 3 , . . . in a specified order.
As an alternative to Definition 8.1, we can also consider a sequence to be a function f