Sequences and Series Review

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geometric series formula

Sn=a1(1-r^n)/1-r READ: the sum of n terms of a geometric series is equal to the first term multiplied by 1 minus the common ratio raised to the n power all divided by 1 minus the common ratio.

arithmetic series formula

Sn=n[(a1+an)/2] READ: The sum of n terms of an arithmetic series is equal to the number of terms multiplied by the average of the first term and the last term.

Two things that must be given for a recursive formula:

1: first term 2: pattern rule

All infinite arithmetic series _________

DIVERGE

convergent series formula

S=a1/(1-r) READ: The sum of the infinite series is equal to the first term divided by 1 minus the common ratio.

What three things must be true for you to be able to determine the sum of an infinite series?

The series must be: 1. geometric 2. infinite 3. convergent

typical element

a general explicit formula for evaluating a specific term in a given series

arithmetic sequence

a sequence in which each term is found by adding or subtracting the same number from the previous term

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number

sequence

an ordered list of numbers 2, 4, 6, 8

series

an ordered sum of numbers 2+4+6+8

formula used to evaluate a term in an arithmetic sequence or series

an=a1+d(n-1) READ: Term n is equal to the first term plus the common difference times n minus 1.

formula used to evaluate a term in a geometric sequence or series

an=a1xr^n-1 READ: Term n is equal to the first term times the common ratio raised to the n-1 power. NOTE: Only the common ratio is raised to the n-1 power, not the entire right side of the formula.

common difference notation

d

upper bound

end term of a series summation

What function familay are geometric sequences and series related to?

exponential functions

"a sub 1"

first term of the sequence or series

What do you underline when annotating?

important/signal words NOTE: this includes things like units

What function family are arithmetic sequences and series related to?

linear functions

What do you circle when annotating?

numbers and number words

common ratio notation

r

index

start term of a series summation

sigma

sum NOTE: Sigma should automatically signal to you that you must find a sum. Sigma is only used in reference to series.

The sum of a divergent series is _________

sum does not exist OR sum DNE

A series diverges if _________

the absolute value of the common ratio is greater than 1

A series is convergent if _________

the absolute value of the common ratio is less than 1

common difference

the difference between consecutive terms of an arithmetic sequence

What do you box when annotating?

the question NOTE: this should tell you form your answer should take

common ratio

the ratio of successive terms of a geometric sequence

"a sub n" or "term n"

the term for which you are evaluating

n

the term number for which you are evaluating (sequences) OR the number of terms (series)


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