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23 Cards in this Set
 Front
 Back
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 + (n1)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 + (n1)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^n1 

Formula for sum of geometric sequences 
Sn = u1(1r^n) / 1r where r does not equal 1 or Sn = u1(r^n1) / r1 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 / 1r 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 