Stefen McCone
A geometric sequence is a sequence with the ratio between two consecutive terms. Also called the common ratio.



Geometric Sequences:


What is a geometric sequence?
A geometric sequence is a sequence that has a generator that is either multiplication or division.

What does its graph look like?
Its graph is a curve, much resembling half of a parabola.

What is the equation?
Initial Term+ Generator (To The Power of the Term That You Are Solving For)= Output

What do the terms look like?
The terms do not have a constant difference, but their generators have a common multiple.

What do the staircases mean?
The staircases are the differences between the terms.

What does the initial value mean?
The initial value is also the y-intercept.



Marjorie Moreno
Geometric sequence is a sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio. It is obvious that a ≠ 0 and r ≠ 0 or 1.
1, 2, 4, 8, 16, 32, . . . is a geometric sequence.
Each term of this geometric sequence is multiplied by the common ratio 2.

Geometric series is the indicated sum of the terms of a geometric sequence.
For the geometric sequence 1, 2, 4, 8, 16, 32,
1 + 2 + 4 + 8 + 16 + 32 is the corresponding geometric series.

Practice:
Find the 5th term and the common ratio 2,6,18
Choices:
A. 54
B. 3
C.162
D. 164
Correct Answer: C
Solution:
Step 1: the common ratio is 3. 2(3) = 6 6(3) = 18
Step 2: so r = 3 the 4th term would be 18(3) = 54
the 5th term would be 54(3) = 162