May 23, 2012
May 23, 2012
Arithmetic Sequence:
has the form: {a, a + d, a + 2d, a + 3d, ... a + (n-1)d, ...},
for some constant, d (called the common difference).
Recursive Formula:
an = an-1 + d (for all n > 2)
7, 10, 13, 16, ...
n
1
2
3
4
n
Term
a
1
May 23, 2012
For each of the following arithmetic sequences, find
a. the common difference
b. the tenth term
c. a recursive rule for the nth term
d. an explicit rule for the nth term
1.
2.
5, 8, 11, 14, 17, ...
ln 3, ln 9, ln 27, ln 81, ...
May 23, 2012
Geometric Sequence:
has the form {a, ar, ar2, ar3, ... arn-1, ...} for some
nonzero constant r (common ratio).
an = an-1 r
n
1
2
3
4
n
Value
a1
(for all n > 2)
May 23, 2012
For each of the following geometric sequences, find
a. the common ratio
b. the tenth term
c. a recursive rule for the nth term
d. an explicit rule for the nth term
1.
2, 6, 18, 54, 162, ...
2.
26, 29, 212, 215, 218, ...
May 23, 2012
Constructing Sequences
1. The second and fifth terms of a sequence are 3 and 192,
respectively. Find explicit and recursive formulas for the
sequence if it is
a. arithmetic
b. geometric