Sequences and Series
Infinite Geometric Series Formula
*Only if |r| < 1*
Find the Sum of the Geometric Series - 3 + 0.3 + 0.003 + ...
10/3
Recursive Arithmetic Sequence Example: First term: 5, Common difference: 2. Find 4th term
11
Find the n = 20 term in the following Arithmetic Sequence. 25, 50, 75, 100, 125, ...
500
What is the sum of the nth term? 2, 8, 32, 128, ... n=9
A(9)=131,072
Sum of an Infinite Geometric Sequence
Can only be done if the r value is less than one
Converging & Diverging Geometric Sequences
Diverging: Increasing Converging: Decreasing You can find the sum of an infinite geometric series if the r value is less than 1.
Geometric Sequence Definition
Is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Determine whether the sequences is arithmetic, if so find the common difference. 2, 4, 8, 16, 32
Not arithmetic
Arithmetic Sequence
Numbers that
Geometric Series Definition
Sum of a geometric sequence
Find the recursive equation for this Geometric Sequence 0.2, -1, 5, -25, ...
a(n)=a(n-1)*(-5)
Arithmetic Recursive Equation
an = nth term, a1 = first term, d = common difference
Find the Sum of the Geometric Series - 4(.3) + 4(.3)^2 + 4(.3)^3 + ... + 4(.3)^12
~1.714