Algebraic Sequences

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This is a lesson/slideshow presentation I made for my 8th grade PreAlgebra students.

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Algebraic Sequences

  1. 1. Algebraic Sequences Obj. Generate an algebraic expression given part of a sequence.
  2. 2. Algebraic Sequence <ul><li>A sequence which has a constant difference between terms. </li></ul><ul><li>Examples: </li></ul><ul><li>1, 5, 9, 13, 17 </li></ul><ul><li>-7, -1, 5, 11, 17 </li></ul><ul><li>21, 20, 19, 18, 17 </li></ul>
  3. 3. EXAMPLE 1 Write an expression for the n th term in the sequence 3, 4, 5, 6, 7, …? Step 1 :  Construct a process chart showing the position and the corresponding term. 3 4 5 6 7 +1 +1 +1 +1 Position “ 0” 1 2 3 4 5 n Term
  4. 4. Determine the common difference (the change) of the terms. STEP 2 Common Difference: 1 This is the coefficient of n . 1 n
  5. 5. Reverse the pattern to find the “zero” term. STEP 3 3 4 2 5 6 7 -1 Zero term: 2 Position “ 0” 1 2 3 4 5 n Term
  6. 6. Common Difference: 1 FINISHING IT OFF Zero Term: 2 1 2 n + 2 n +
  7. 7. EXAMPLE 1 Write an expression for the n th term in the sequence 12, 8, 4, 0, -4, …? Step 1 :  Construct a process chart showing the position and the corresponding term. 12 8 4 0 -4 -4 -4 -4 -4 Position “ 0” 1 2 3 4 5 n Term
  8. 8. Determine the common difference (the change) of the terms. STEP 2 Common Difference: -4 This is the coefficient of n . -4 n
  9. 9. Reverse the pattern to find the “zero” term. STEP 3 12 8 16 4 0 -4 +4 Zero term: 16 Position “ 0” 1 2 3 4 5 n Term
  10. 10. Common Difference: -4 FINISHING IT OFF Zero Term: 16 -4 16 -4 n + 16 n +
  11. 11. Practice <ul><li>4, 9, 14, 19, 24 </li></ul><ul><ul><li>5n + -1 or 5n - 1 </li></ul></ul><ul><li>-8, -5, -2, 1, 4 </li></ul><ul><ul><li>3n + -11 or 3n – 11 </li></ul></ul><ul><li>7, 1, -5, -11, -17 </li></ul><ul><ul><li>-6n + 13 </li></ul></ul><ul><li>-15, -11, -7, -3, 1 </li></ul><ul><ul><li>4n + -19 or 4n – 19 </li></ul></ul>

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