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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?


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?


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 1


Sn = 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