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.

   Ari's phone-tree chart for a club picnic shows the list 4, 12, 36, 108. Is the list arithmetic, geometric or neither?

   • Geometric: × 3 on every arrow
   • Arithmetic: + 8 on every arrow
   • Neither: the arrows change
2. 2.

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

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

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

   • Arithmetic: − 54 on every arrow
   • Geometric: × 1/3 on every arrow
   • Neither: the arrows change
4. 4.

   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
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.

   Zee's phone game scores grow. The rule is a(1) = 2, a(n) = 5 · a(n − 1). What is a(4)?

   250
8. 8.

   Bo reads 12 pages on day 1 of a reading challenge, then 5 more pages each day than the day before. How many pages does Bo read on day 6?

   37
9. 9.

   A science video shows 300 bacteria in a dish at count 1. The number doubles (× 2) at each count, 20 minutes apart. How many bacteria does Kira see at count 5?

   4800
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