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Chapter 1 Nth Term

Chapter 1 Nth Term. I Can . . . State a rule to find the nth term of a pattern using variables. Identify and continue arithmetic patterns using an equation. HW: Teacher W.S. Arithmetic Sequences. Arithmetic Sequence: A pattern of numbers with a common difference between each number.

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Chapter 1 Nth Term

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  1. Chapter 1 Nth Term I Can . . . State a rule to find the nth term of a pattern using variables. Identify and continue arithmetic patterns using an equation. HW: Teacher W.S.

  2. Arithmetic Sequences Arithmetic Sequence: A pattern of numbers with a common difference between each number. Term: Each number in a sequence Common Difference: The change added between each term in the sequence, which represents the rate of change or “a” Zero Term: The number that comes before the first listed term in the sequence, or “b”

  3. Finding the Nth Term Addition Steps Step 1: Find 2nd Term – 1st Term Finds the common difference “a” 59, 48, 37, 26, . . . zero 1 2 3 4 70 48 – 59 = 48 + -59 = -11 thereforea = -11 -11 -11 -11 -11 Step 2:Take 1st Term – a Finds the zero term “b” a = -11 Nth Term Rule 59 – (-11) = 59 + 11 = 70 therefore b = 70 b = 70 an + b -11n + 70 Step 3: Write the expression in an + b form -11n + 70

  4. Student Practice Problems 1. 12, 16, 20, 24, . . . 2. 32, 26, 20, 14, . . .

  5. #3 & 4 • 3) 5, 8, 11, 14, ……… • 4) 14, 12, 10, 8……..

  6. Changing Nth Term to an Equation To write an equation for the Nth term, simply change the “n” to “x”, and write it as y = Example: 24, 12, 0, -12, -24, . . . a = -12 -12 b = 36 36 Nth Term: an + b -12n + 36 Equation: y = ax + b y = -12x + 36

  7. Application to Word Problems Joe is a plumber. He charges $40 for a service charge plus $30 for each hour he works. How much will he earn for an 8 hour day at the same job? a = 30 b = 40 Pattern: 40, 70, 100, 130, . . . 30 Zero 1 2 3 Nth Term: 30n + 40 Equation: y =30x + 40 y = 30(8) + 40 y = 240 + 40 y = 280 Solve for x = 8

  8. Nth Term Activity Cards Choose a sequence card. Find the equation card that describes the sequence card. After matching all the cards, get the answer key from the front desk. 2, -2, -6, . . . y = -4x + 6 -3, 11, 25, . . . y = 14x + -17

  9. Closure Consider the Nth Term expression: an + b Partner 1: Explain how to find the “a” part of the Nth term expression. Partner 2: Explain how to find the “b” part of the Nth term expression.

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