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### 23 Cards in this Set

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