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

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Every arrow between rows: + 6. Ari's bean plant grows the same amount each week. The growth table shows its height in cm. What is term 6?

   35
2. 2.

   Every arrow between rows: × 2. Bo folds a sheet of paper in half, again and again. The growth table shows how many layers there are after each fold. What is term 6?

   64
3. 3.

   Every arrow between rows: − 4. Esme hands out star stickers each round. The growth table shows how many are left after each round. What is term 6?

   11
4. 4.

   Every arrow between rows: × 3. Jun builds a block pattern that grows by the same factor. The growth table shows the blocks in each stage. What is term 6?

   486

5. Read this first

   Growth table

   term number n	term
   1	450
   2	380
   3	310
   4	240

6. 5.

   Kira drinks the same amount of water between stops on a hike. The growth table shows the mL left at each stop. Every arrow adds the same number. What number goes on each arrow?

   -70
7. 6.

   Noah draws a star pattern for art club. The growth table shows the stars in each stage. Every arrow multiplies by the same number. What number goes on each arrow?

   4
8. 7.

   Pia's pencil-case pattern uses the rule a(n) = a(n − 1) + 7, with a(1) = 4. So a(2) = 4 + 7 = 11. What is a(4)?

   25
9. 8.

   Ren's robot's number game uses the rule a(n) = 2 · a(n − 1), with a(1) = 5. So a(2) = 2 · 5 = 10. What is a(5)?

   80
10. 9.

    Tala's countdown game uses the rule a(n) = a(n − 1) − 3, with a(1) = 40. So a(2) = 40 − 3 = 37. What is a(6)?

    25
11. 10.

    Zee's drum-beat pattern uses the rule a(n) = 4 · a(n − 1), with a(1) = 3. So a(2) = 4 · 3 = 12. What is a(4)?

    192