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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 1




or




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