Recursive Formulas Worksheet with Answer Key

What's on the worksheet

1. Write the first four terms for each recursive rule.
   a_1 = -8, a_n = a_{n-1} + 6a_1 = 0.5, a_n = 4 \cdot a_{n-1}f(1) = -48, f(n) = -\dfrac{1}{4} \cdot f(n-1)a_1 = 1.5, a_n = a_{n-1} - 0.4a_1 = 2, a_n = 10 - 2 \cdot a_{n-1}
2. Test differences or ratios, then write a recursive formula for each sequence.
   −11, −4, 3, 10, …1.5, 6, 24, 96, …243, −81, 27, −9, …\dfrac{5}{2}, 2, \dfrac{3}{2}, 1, \dots
3. Rewrite a function-notation recursive rule in subscript notation and use it.
4. Find the fixed number c in a doubling rule from the third term.
5. Write terms of a half-and-add rule from different starting values.
6. Daily medicine dose: model the amount in the body with a recursive rule.