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# Math1050 CH09

### Sequences

Side 1Side 2
A sequence is a function whose domain is ___. the set of positive integers
The domain is also called the ___. inputs
We use ___ to represent the independent variable of a sequence. n
The outputs of a sequence are called ___. terms
The formula for the nth term is called the ___. general term
To represent the entire sequence we place ___ around the formula for the general (nth) term. braces
Factors such as (-1)^n+1, causes the signs of the terms to ___. alternate
A number multiplied by each successive smaller positive integer is called a ___. factorial
A factorial uses the symbol ___. n!
A factorial is defined as 0!=___, 1!=___, n!=___. 1, 1, n(n-1)(...)(3)(2)(1)
100!/98!=___. (100)(99)=9900
(3)(2!)=___. 3!=6
Assigning a value to the first term and listing the nth term is called a ___. recursive formula
The recursive formula, u_1 = 1, u_2 = 1, u_n = u_n-2 + u_n-1, is the ___ sequence. Fibonacci
In summation notation, k is the ___. It tells you ___. index, where to start and end the sequence
In summation notation, below the sigma tells you where to ___ the sequence and below tells you where to ___ it. start, end
In summation notation, to the right of the sigma is the ___. sequence fomula
Summation notation tells us the ___. sum of the first n terms
In summation notation, what does it mean when letters other than k are used? Nothing.
When the difference between successive terms of a sequence is always the same, the sequence is ___. arithmetic
An arithmetic sequence may be defined recursively as ___. a_1 = a, a_n = a_n-1 + d
In an arithmetic sequence d is ___. the common difference (between each successive output)
In an arithmetic sequence a is ___. the first term
The nth term is a way of saying ___. any number in the sequence
The formula for the nth term of an arithmetic sequence is ___. a_n = a_1 + (n-1)d
Using the formula for the nth term of an arithmetic sequence, a_41 = a_1 + (___)d. 40
What are the 2 formulas for the sum of the first n terms of an arithmetic sequence? n/2(2a_1 + (n-1)d) or n/2(a_1 + a_n)
A sequence is geometric if the ___ of successive terms is always the same. ratio
A geometric sequence is defined recursively as ___. a_1 = a, a_n = ra_n-1
In a geometric sequence the formula for r is ___. r = a_n/a_n-1 (a term divided by the preceding term)
For a geometric sequence, r is called the ___. common ratio
The nth term of a geometric sequence is defined by the formula a_n = ___. (a_1)r^n-1
For a geometric sequence, the sum of the first n terms is defined by the formula S_n = ___. a_1((1 - r^n)/(1-r))
For a geometric sequence, if a finite sum S_n approaches a number L as n approaches infinity, then the series ___. converges
For a converging series, we call L the ___. sum of the geometric series
If a geometric sequence doesn't converge then it ___. diverges or is divergent
For a converging series, r is always a ___. proper fraction
What is the series for the repeating decimal 0.999...? What is r? What is a_1? 0.9 + 0.09 + 0.009 + ... or 9/10 + 9/100 + 9/1000 + ..., r = 1/10, a_1 = 9/10^k
Created by: drjolley