1. Lesson 2.6 Geometric Sequences
By Daniel Christie

2. Homework
Page

3. Explained: Geometric Sequences
A sequence is geometric if the quotient between a term in the sequence and it’s previous term is a constant [usually called a common ratio]
Example: u2/u1 = u3/u2 = u4/u3 = r
Or: 2/1 = 4/2 = 8/4 = 16/8 = 2
Explanation: The common ratio is 2 because every fraction in the set equals 2.

4. General Term of a Geometric Sequence
u2 = u1 x r u3 = u2 x r = u1r2 u4 = u3 x r = u1 r3 and in general… un = u1 x rn-1

5. Application of Geometric Sequences
Problem: A car costs $ It loses 20% value every year. How much is the car worth in 6 years?
Un is the number of years. 0.8 is the common ratio.
Un = n * rn-1
Special case for problems with yearsUn = n * rn
Special case for problems with years SEE BELOW
Example: u1 = x 0.8 = : u2 = x 0.82 = 28800
u6 = x 0.86 = 11,796

6. Geometric Series: Sum of the Terms in a Geometric Sequence
Sn = the sum of the geometric sequence
Equations:
Sn = u1 (rn - 1 )
n = what power in series = 5th
r - 1
u1 = 1st term in series = 2
Sn = u1 (1 - rn)
rn = ratio to what power = 2 5
r = 2
(2, 4, 8, 16, 32)
(1st , 2nd , 3rd , 4th , 5th)

7. Geometric Series: Sum of the First n Terms of a Geometric Sequence
An example geometric series: 1,2,4,8,16,32,64,128
Example: …+263
2s = … [s-1]
2s = s-1+264
2s-s =
s = 264-1
s = 1.84 x 1019

8. Pictures by Daniel Christie
Thank You
Pictures by Daniel Christie