Closed Form Versus Recursive Form Worksheet with Answer Key

What's on the worksheet

1. Write each sequence in the other form, explicit or recursive.
   a_1 = 9, \; a_n = a_{n-1} - 5a_n = 6n - 11a_1 = 5, \; a_n = -2a_{n-1}a_n = 48\left(\dfrac{1}{2}\right)^na_n = \dfrac{n + 3}{2}
2. Write an explicit formula for a recursive rule and count its terms.
3. Use an arithmetic recursive rule and one term to find other terms.
4. Decide which explicit formulas describe the same sequence.
5. Trout pond model: use the explicit formula and write the recursive rule.
6. Check two students' conversions between forms and find the errors.
7. Find the constants that make an explicit formula and a recursive rule match.