Chapter 11: Sequences & Series Flashcards
To identify mathematical patterns, to identify and generate arithmetic/geometric sequences and series, to evaluate and write sequences and series..etc.
Define “sequence”
An ordered list of numbers
Define “recursive formula”
A recursive formula defines terms in a sequence by relating each term to the ones before it.
Define “explicit formula”
A formula that expresses the nth term in terms of n is an explicit formula.
In an arithmetic sequence, the difference between consecutive terms is ______.
constant
Define “common difference”
The difference between consecutive terms in an arithmetic sequence.
How do you find the arithmetic mean between two numbers?
You add the two numbers and divide by two.
The constant ratio between consecutive terms in a geometric sequence is called the ______.
Common ratio.
Arithmetic sequence - Recursive formula
a-sub-1= a given value, a-sub-n = a-sub-n-1 + d
Arithmetic sequence - Explicit formula
a-sub-n = a-sub-1 + (n-1)d
Geometric sequence - Recursive formula
a-sub-1= a given value, a-sub-n = a-sub-n-1 * r
Geometric sequence- Explicit formula
a-sub-n = a-sub-1 *r^n-1
What is the d symbolizing in an arithmetic sequence and series?
common difference
What does the r symbolize in a geometric series and sequence?
common ratio
Formula for evaluating an arithmetic series
S-sub-n =n/2(a-sub-1 + a-sub-n)
A-sub-1
first term
A-sub-n
nth term
Define “Limits”
Limits are the least and greatest integral values of n.
How do you write a Summation Notation?
It is the letter Sigma, on top is the upper limit (highest number of terms) on bottom, is the lower limit (least number of terms) and the explicit formula is given on the side.
Formula for evaluating a geometric series:
S-sub-n = a-sub-1(1-r^n)/(1-r)
When a geometric series converges, it…
gets closer and closer to 0 meaning r is less than 1
When r is greater than 1…
It has no limit therefore it is impossible to evaluate.
The formula for evaluating an infinite geometric series when r is less than one
S= a-sub-1/1-r
