Number Patterns (Sequences)

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Presentation transcript:

Number Patterns (Sequences) We are learning to…analyze patterns and predict numbers in sequences. Sunday, April 23, 2017

__________________________ Silent Function Game X 4 5 1 3 10 Y 23 398 7 79 Rule: __________________________

Vocabulary for Patterns and Sequences Term - a number or object in a sequence Linear Sequence – a pattern in which the next term increases or decreases by the same amount (constant rate of change) Non-Linear Sequence – a pattern in which the next term does not increase or decrease by the same amount (varying rate of change)

Analyze the pattern: 2, 4, 6, 8, 10… The pattern is linear, because it demonstrate a constant rate of change. The pattern starts at 2 and increases at a constant rate of 2. The next 5 terms of the pattern are: …12, 14, 16, 18, 20.

Analyze the pattern: 2, 4, 6, 8, 10… The pattern is linear, because it demonstrates a constant rate of change. The pattern starts at 2 and increases at a constant rate of 2. The next 5 terms of the pattern are: 2, 4, 6, 8, 10… 12, 14, 16, 18, 20…

Analyze the pattern: 2, 5, 10, 17, 26… The pattern is non-linear, because it does not demonstrate a constant rate of change. The pattern starts at 2 and increases by consecutive odd numbers. The next 5 terms of the pattern are: 2, 5, 10, 17, 26… 37, 50, 65, 82, 101…

Analyze the pattern: 1, 4, 7, 10, 13… The pattern is linear, because it demonstrates a constant rate of change. The pattern starts at 1 and increases at a constant rate of 3. The next 5 terms of the pattern are: 1, 4, 7, 10, 13… 16, 19, 22, 25, 28…

Patterns and Functions Think of a sequence as just the outputs of a function.

Put the pattern 2, 4, 6, 8, 10… in the input/output table below. X 1 2 3 4 5 Y 2 4 6 8 10 What is the function (numerical expression) that will model the input/output table? _______________________ Use this function to predict the 25th term of the sequence. Use this function to predict the 52nd term of the sequence The 25th term of the sequence is 50! The 52nd term of the sequence is 104!

Put the pattern 2, 5, 10, 17, 26 … in the input/output table below. X 3 4 5 Y 2 5 10 17 26 What is the function (numerical expression) that will model the input/output table? _______________________ Use this function to predict the 15th term of the sequence. Use this function to predict the 100th term of the sequence The 15th term of the sequence is 226! The 100th term of the sequence is 10,001!

Put the pattern 1, 4, 7, 10, 13… in the input/output table below. X 1 2 3 4 5 Y 1 4 7 10 13 What is the function (numerical expression) that will model the input/output table? _______________________ Use this function to predict the 250th term of the sequence. Use this function to predict the 1000th term of the sequence The 250th term of the sequence is 748! The 1000th term of the sequence is 2998!

Assessment Analyze the pattern: 7, 12, 17, 22, 27…