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3.5 Arithmetic Sequences as Linear Functions Objective: 1) Use inductive reasoning in continuing number patterns 2) Write rules for arithmetic sequences 3) Relate arithmetic sequences to linear functions Vocabulary • Inductive reasoning: Making conclusions based on patterns you observe. • Sequence: a set of numbers in a specific order • Terms: the numbers in a sequence Vocabulary Continued • Arithmetic Sequence: A numerical pattern that increase or decrease at a constant rate or value. • Common Difference: The difference between the terms in a sequence. Represented by the letter d. Find the next two numbers in each pattern and describe the pattern a) 2, 5, 8, 11,… b) 2, 4, 6, 8,… c) 1, 9, 17, 25, … Determine whether the sequence is an arithmetic sequence if so what is the pattern? -4, -2, 0, 2,… Determine whether the sequence is an arithmetic sequence if so what is the pattern? -26, -22, -18, -14,… Determine whether the sequence is an arithmetic sequence if so what is the pattern? 1, 4, 9, 25, … Determine whether the sequence is an arithmetic sequence if so what is the pattern? 1 5 3 13 , , , ,... 2 8 4 16 Find the nth term an a1 (n 1)d a1= first term of sequence d= common difference **** n must be positive **** Write an equation for the nth term of the arithmetic sequence -12, -8, -4, 0, … Find the th 9 term of the sequence Which term of the sequence is 32? You Try Consider the arithmetic sequence 3, -10, -23, -36, … a) Write an equation for the nth term of the sequence b) Find the 15th term in the sequence c) Which term of the sequence is –114? Arithmetic Sequences as Functions Marisol is mailing invitations for her quinceanera. The arithmetic sequence $0.41, $0.82, $1.23, $1.64, … represents the cost of postage. a) Write a function to represent this sequence Write an arithmetic sequence on a blank piece of paper.