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23 Cards in this Set
- Front
- Back
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Definition of a sequence |
A list of numbers that follows a pattern |
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In the notation for the term of a sequence, the subscript represents... |
The position where the term is in the sequence |
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What is a series? |
The sum of the numbers in a sequence up to a given point |
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The type of sequence where there is a constant/common difference between consecutive terms |
Arithmetic sequence (or arithmetic progression) |
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What is the standard notation for the difference between terms in an arithmetic sequence? |
d |
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The formula for the general term in an arithmetic sequence
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un = u1 + (n-1)d |
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What symbol is used to denote the sum of the first 'n' terms of a sequence? |
Sn |
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Formula for the sum of an arithmetic series if you know the first and last terms |
Sn = n/2(u1+un) |
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Formula for the sum of an arithmetic series if you know the first term and the common difference |
Sn = n/2 (2u1 + (n-1)d) |
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Type of sequence that has a constant/common ratio, r, between terms |
Geometric sequence |
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Formula for the general term of a geometric sequence |
un = u1r^n-1 |
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Formula for sum of geometric sequences |
Sn = u1(1-r^n) / 1-r where r does not equal 1 or Sn = u1(r^n-1) / r-1 where r does not equal 1 |
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A series in which its sum grows or decreases without limit |
Divergent series |
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A series in which its sum gets closer and closer to a finite number |
Convergent series |
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Formula for sum to infinity of a geometric series |
u1 / 1-r if the absolute value of r is less than 1 |
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Compound interest follows what kind of sequence? |
Geometric sequence
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Alternate notation for the sum of a series |
Sigma notation |
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When given a term that is not the first term, always rewrite Un as |
U1, U1+d, U1+2d etc U1, U1r, U1r^2 etc |
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Look out for this word that contains a hidden sum |
'The average of n values is... |
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If a question asks for what value does a series converge you need to solve for |
abs r is less than one |
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If you have a sequence written in fractions treat the numerator and denominator as |
separate sequences (unless it obvious) |
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How to spot a quadratic sequence |
The difference between the differences will be equal. Look at the second line of differences |
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How to find a quadratic sequence general term |
Use an^2+bn+c and find f(1), f(2), f(3). Solve the 3 x 3 system of equations to find a, b and c. Do this on plysmlt 2 |
