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ARITHMETIC SEQUENCES Explicit Formula

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ARITHMETIC SEQUENCE A sequence of numbers where each number is increased or decreased by the same amount to get the next term A sequence of numbers where each number is increased or decreased by the same amount to get the next term The same amount is often known as the common difference (d) The same amount is often known as the common difference (d)

Slide 3

PRACTICE 2, 5, 8, 11, 14, ____,____,_____ 2, 5, 8, 11, 14, ____,____,_____ What are the missing numbers? What are the missing numbers? What is the common difference? What is the common difference?

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PRACTICE -1, -6, -11, -16, -21, ____,____,____ -1, -6, -11, -16, -21, ____,____,____ What are the missing numbers? What are the missing numbers? What is the common difference? What is the common difference?

Slide 5

WHAT IF I WANT THE 50 TH TERM?

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2, 5, 8, 11, 14 2 nd term has 1 three 3 rd term has 2 threes 4 th term has 3 threes 5 th term has 4 threes See a pattern?

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THE FORMULA

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Any term Multiply by one less than whatever term you want 1st term Common Difference

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THE EXPLICIT FORMULA

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Slide 12