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Mastering Recursive Formulas in Advanced Math

Learn how to use recursive formulas to find the nth term in sequences, step by step examples provided. Includes word problems and homework exercises.

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Mastering Recursive Formulas in Advanced Math

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  1. Lesson 4.3: Using Recursive Formulas Advanced Math Topics

  2. Definition of Recursive Formula • The formula for a sequence that tells you how to find the nth term from the term(s) before it.

  3. Example/Steps • Part 1: the value of the 1st term(s) are given • a1 = 1 • Part 2: A recursion equation shows how to find each term from the term before it. • an=2an-1 • Part 3: Plug numbers into the formula to find the next terms in the sequence. • a2=2a2-1=2a1=2(1)=2 • a3=2a3-1=2a2=2(2)=4 • a4=2a4-1=2a3=2(4)=8

  4. Examples • a1=12 • an=3(an-1) n

  5. Examples • a1=3 • a2=2 • an=an-1-2an-2

  6. Examples • a1=1 • a2=2 • an=(an-2)2-(an-1)2

  7. Examples • a1=10 • an= 1 an-1

  8. Word Problem • Start January by plugging in 0 for an-1 and then fill in chart

  9. Homework • Page 225/ 8-13 • Remember that i is an imaginary number and i2 = -1

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