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

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Esme's bake-sale tally shows the list 2, 6, 18, 30. Is the list arithmetic, geometric or neither?

   • Geometric: × 3 on every arrow
   • Neither: the arrows change
   • Arithmetic: + 4 on every arrow
2. 2.

   Jun's math-club handout shows the list 81, 27, 9, 3. Is the list arithmetic, geometric or neither?

   • Neither: the arrows change
   • Arithmetic: − 54 on every arrow
   • Geometric: × 1/3 on every arrow
3. 3.

   Luz's class uses a phone tree for a trip. The people told in rounds 1 to 4 are 5, 10, 20, 40. What is the next term?

   80
4. 4.

   Milo cuts a ribbon in half again and again, keeping one half. The lengths in cm are 96, 48, 24, 12. What is the next term?

   6
5. 5.

   Noah's robot token jumps the same amount each turn on a number line. Its spots are 14, 9, 4, -1. What is the next term?

   -6
6. 6.

   Pia's quiz-game score changes by the same amount each round. The scores are 10, 4, -2, -8. What is the next term?

   -14
7. 7.

   Ren climbs a pretend number ladder. The rule is a(1) = 6, a(n) = a(n − 1) + 9. What is a(5)?

   42
8. 8.

   Ari draws a tree whose branches split. The rule is a(1) = 4, a(n) = 3 · a(n − 1). What is a(5)?

   324
9. 9.

   Esme's school hall has 14 chairs in row 1, and each row has 2 more chairs than the row before. How many chairs are in row 8?

   28
10. 10.

    Luz drops a play ball from shoulder height. Bounce 1 reaches 80 cm, and each bounce is 1/2 as high as the one before. How high, in cm, is bounce 4?

    10