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The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph.
f(a)-f(b)/a-b

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Explains how to set up arithmetic and geometric sequences using sequence of numbers.

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Arithmetic & Geometric Sequences & Series Review Sigma Noation & Word Problems

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d=# of jumps√Last/First
Used to find missing numbers in a geometric table.

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d=Last-First/# of jumps
Used to find missing numbers in a arithmetic table

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∑ x
n=1
Used as a convenient and simple form of shorthand used to give a concise expression for a sum of the values of a variable.

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Recursive: f(n)=f(n-1)+d
Use to find the next number in a arithmetic sequence using the previous number and a common difference.
Explicit: f(n)=f(1)+(n-1)d
Used to find any number using a common difference in a arithmetic sequence.

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Recursive: f(n)=f(n-1)d
Used to find the next number using the previous number in a geometric sequence and a common ratio.
Explicit: f(n)=f(1)r^(n-1)
Used to find any number in a geometric sequence using a common ratio.

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-Arithmetic Sequence: a sequence of numbers such that the difference between the consecutive terms is constant.
-Geometric Sequence: a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
-Common Ratio: the ratio of a term to the previous term.
-Common Difference: the difference between two numbers in an arithmetic sequence.
-Explicit: an equation to represent the nth term of the sequence.
-Recursive: an equation that is used to determine the next term of a sequence using one or more of the previous terms.
-Sum of Sequence: when you add up all the terms in a sequence
-Arithmetic Mean: the average of a set of numerical values, calculated by adding them together and dividing by the number of terms in the set.
-Geometric Mean: the central number in a geometric progression, also calculable as the n the root of a product of n numbers.
-Average Rate of Change: the change in the value of a quantity divided by the elapsed time.
-Discrete: do not connect the dots on a graph; pattern happens only at specific moments.
-Continuous: dots are connected on a graph; pattern constantly happens over time.
-Concave: which way a exponential line is open facing (UP or DOWN)
-Compound Interest: interest in the next period is then earned on the principal sum plus previously-accumulated interest.
-Interest Rate: amount charged, expressed as a percentage of principal.