Notation for Sequences and Examples
We denote the terms of a sequence by
a
1
,
a
2
,
a
3
, . . . ,
a
n
, . . .
so that
a
1
is the first term,
a
2
is the second term, and so on. We
use
a
n
to denote the nth or general term of the sequence. If there
is a pattern in the sequence, we may be able to find a formula for
a
n
.
Example 1
(a) 0, 1, 4, 9, 16, 25, . . . is the sequence of squares of integers.
(b) 2, 4, 8, 16, 32, . . . is the sequence of positive integer powers of 2.
(c) 3, 1, 4, 1, 5, 9, . . . is the sequence of digits in the decimal expansion
of π.
(d) 3.9, 5.3, 7.2, 9.6, 12.9, 17.1, 23.1, 38.6, 50.2 is the sequence of U.S.
population figures, in millions,for the census reports (1790 -1880).
(e) 3.5, 4.2, 5.1, 5.9, 6.7, 8.1, 9.4, 10.6, 10.1, 7.1, 3.8, 2.1, 1.4, 1.1 is the
sequence of pager subscribers in Japan, in millions, from the years
1989 -2002.
Functions Modeling
Change:
A Preparation
for Calculus,
4th