Definitions A SEQUENCE is a list of numbers in a particular order. Each number in a sequence is called a TERM.

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Presentation transcript:

Definitions A SEQUENCE is a list of numbers in a particular order. Each number in a sequence is called a TERM.

Definition – Arithmetic Sequence

SequenceNumber … symbols Number symbols

SequenceNumber … symbols … Number symbols

SequenceNumber … symbols … Number55+1(-6) symbols

SequenceNumber … symbols … Number55+1(-6)55+2(-6) symbols

SequenceNumber … symbols … Number55+1(-6)55+2(-6) symbols

SequenceNumber … symbols … Number55+1(-6)55+2(-6) symbols

SequenceNumber … symbols … Number55+1(-6)55+2(-6)55+3(-6)…55+(n-1)d symbols

SequenceNumber … symbols … Number55+0(-6)55+1(-6)55+2(-6)55+3(-6)…55+(n-1)d symbols…

SequenceNumber … symbols … Number55+0(-6)55+1(-6)55+2(-6)55+3(-6)…55+(n-1)d symbols…

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist?

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference?

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference? -3

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference? -3

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference? -3

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference? -3

Example What is the 15 th term of the sequence 34, 31, 28, … Does a common difference exist? Yes. What is the common difference? -3

Arithmetic Means The terms between any two nonsuccessive terms of an arithmetic sequence are called ARITHMETIC MEANS. In the sequence below 41, 52, and 63 are the three arithmetic means between 30 and 74.

Example – Arithmetic Means

Assignment