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.

   Milo's practice minutes are arithmetic over 4 days: 8, ?, ?, 26. What is the second term?

   14
2. 2.

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

   17
3. 3.

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

   20
4. 4.

   Zee's list is 4, 10, 16, 22. Which recursive rule makes this list?

   • a(1) = 4, a(n) = a(n − 1) + 6
   • a(n) = a(n − 1) + 6, with no a(1)
   • a(1) = 6, a(n) = a(n − 1) + 4
5. 5.

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

   • a(1) = 2, a(n) = 3 · a(n − 1)
   • a(1) = 3, a(n) = a(n − 1) + 3
   • a(1) = 3, a(n) = 2 · a(n − 1)
6. 6.

   Bo's list is 40, 33, 26, 19. Which recursive rule makes this list?

   • a(1) = 40, a(n) = a(n − 1) + 7
   • a(n) = a(n − 1) − 7, with no a(1)
   • a(1) = 40, a(n) = a(n − 1) − 7
7. 7.

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

   • a(1) = 4, a(n) = 5 · a(n − 1)
   • a(1) = 5, a(n) = 4 · a(n − 1)
   • a(1) = 5, a(n) = 1/4 · a(n − 1)
8. 8.

   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) = 1/4 · a(n − 1)
   • a(1) = 64, a(n) = a(n − 1) − 48
9. 9.

   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
10. 10.

    Pia's robot runs a number trick. The rule is a(1) = 5, a(n) = 2 · a(n − 1) − 3. What is a(5)?

    35