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

   11

3. Read this first

   Growth table

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

4. 3.

   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
5. 4.

   Luz's puzzle game gives points for each level. The growth table shows them. Every arrow multiplies by the same number. What number goes on each arrow?

   3
6. 5.

   Milo's class packs boxes for a food drive. The growth table shows the boxes still to pack after each day. Every arrow adds the same number. What number goes on each arrow?

   -9
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