Post on 31-Dec-2015
description
Explicit Formula for Geometric
Sequence
1
1
n
na a r
Where a1 is the first term in the sequence and
r is the common ratio
Geometric Sequence
Example 1: Find the common ratio
r = 2
4 8 16 32, , , ,...2
1
If you get stuck,
try aa
Example 3: Find the common ratio, the explicit formula, and the seventh term. 6, 3, 1.5, 0.75 …
1
1
n
na a r
11
62
n
na
7 1
7 6 0.5a
3 1
.56 2
r or
7 0.094a
Example 4: Find the common ratio, the explicit formula, and the tenth term. -4, -12, -36, -108 …
1
1
n
na a r
14 3
n
na
10 1
10 4 3a
12
34
r
10 78,732a
Example 5 : The fifth term is 1,792. The common ratio is 4. Write the explicit formula.
5 1792 and 5 and 4a n r
17 4
n
na
5 1
11792 4a
1
1
n
na a r
17 a
Example 6 : During the month of October, a few teachers decided to spread some holiday fun by starting a game of getting “boo”ed. On the first day, 3 teachers were given “boo” bags and directions to “boo” 2 other teachers. If every teacher followed the directions to “boo” 2 teachers with candy and a sign, find the following:
a. The explicit formula b. The first 4 terms
1
1
n
na a r
1a r
13 2
n
na
3, 6, 12, 24…
3 2