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Math1050 CH09
Sequences
| Side 1 | Side 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
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