Download Section 11.3 - Madison Local Schools

Algebra 2B
Day 32
11.3 Geometric Sequences

Daily Openers

Go over and collect homework
11.3 Geometric Sequences
geometric sequence – the sequence whose consecutive terms have a common ratio
GEOMETRIC SEQUENCE
The sequence a1, a2, a3, a4, …, an, … is geometric if there is a # such that
a2
 r,
a1
a3
 r,
a2
a4
 r,
a3
where r is the common ratio of the sequence.
Ex. Find the first four terms of the sequence whose nth term is
Ex. Find the first five terms of the sequence whose
nth term of a geometric sequence
(For an explicit function)
nth term of an arithmetic sequence
(For an recursive function)
nth
an  43
1
term is a n  8 
2
n
n
an  a1 r 
n1
an  an1  r n1
Ex. Write an explicit formula for the sequence and generate the first four terms.
a1 = ½ and r = -2
Ex. Is the sequence arithmetic, geometric, or neither? Find d or r.
(a) 4, 12, 36, 108, …
(b) 16, 12, 9, 6¾, …
(c) 1, 4, 9, 16, 25, …
(d) 10, 0.5, -9, -18.5, …
Ex. Find the 15th term of the G.S. whose first term is 20 and common ratio is 1.05
Ex. Find the 12th term of the G.S. whose first three terms are 5, 15, and 45.
Ex. Find
a10 of the geometric sequence with a1  4 and r = ½
Ex. Write a formula for the nth term of the G.S.:
4, 6, 9, 27 , ...
2
Ex. Find the missing term.
a1  4
a5  324
a8  ?
GEOMETRIC MEAN =
product of the two numbers
Ex. Find the geometric mean of 6 and 24
Ex. Find the missing term of the geometric sequence.
4, ▒ , 9
Ex. Find the missing terms of the geometric sequence.
2, ▒ , ▒, ▒, 288
Homework – pages 614-615 #1-55 Odd
Daily Openers – 1. Write an equation of a circle with r = 8 and center at (-3, 6.5)
2. Write an equation of a parabola with vertex: (-2, 3) and focus: (-2, 5)
3. Write an explicit formula for the sequence: 17, 8, -1, …
4. Write a recursive formula for the sequence in #4
5. Find all asymptotes for the function: y 
2x
3x( x  4)