Arithmetic, geometric or neither? Find the next terms with a recursive rule

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Noah's piano practice list is arithmetic: 5, ?, ?, 41. What is the second term?

   17
2. 2.

   Pia's crayon box count is arithmetic over 4 weeks: 50, ?, ?, 14. What is the second term?

   38
3. 3.

   Ren's flower count is geometric: 4, ?, 100. Every term is positive. What is the missing term?

   20
4. 4.

   Ari's list is 3, 6, 12, 24. Which recursive rule makes this list?

   • a(1) = 3, a(n) = a(n − 1) + 3
   • a(1) = 3, a(n) = 2 · a(n − 1)
   • a(1) = 2, a(n) = 3 · a(n − 1)
5. 5.

   Esme's list is 5, 20, 80, 320. Which recursive rule makes this list?

   • a(1) = 5, a(n) = 4 · a(n − 1)
   • a(1) = 5, a(n) = 1/4 · a(n − 1)
   • a(1) = 4, a(n) = 5 · a(n − 1)
6. 6.

   Jun's list is 64, 16, 4, 1. Which recursive rule makes this list?

   • a(1) = 64, a(n) = 4 · a(n − 1)
   • a(1) = 64, a(n) = a(n − 1) − 48
   • a(1) = 64, a(n) = 1/4 · a(n − 1)
7. 7.

   Kira's list is 90, 75, 60, 45. Which recursive rule makes this list?

   • a(1) = 90, a(n) = a(n − 1) − 15
   • a(1) = 15, a(n) = a(n − 1) − 90
   • a(1) = 90, a(n) = a(n − 1) + 15
8. 8.

   Luz's rocket game doubles the score and then takes 1 away each round. The rule is a(1) = 3, a(n) = 2 · a(n − 1) − 1. What is a(4)?

   17
9. 9.

   Milo's star chart triples the stars and then adds 1 each week. The rule is a(1) = 2, a(n) = 3 · a(n − 1) + 1. What is a(4)?

   67
10. 10.

    Noah writes a number trick on paper at math club. The rule is a(1) = 1, a(n) = 2 · a(n − 1) + 4. What is a(5)?

    76