Formulas for the nth term of arithmetic and geometric sequences

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Zee's piano-key pattern: 15, 20, 25, … Which term number is 250?

   48
2. 2.

   Ari's toy-train track pieces: 18, 24, 30, … Which term number is 330?

   53
3. 3.

   Esme's star-pattern stages: 4, 12, 36, … Which term number is 972?

   6
4. 4.

   Jun's hiking map marks an arithmetic sequence with a(3) = 10 and a(9) = 52. What is a(1)?

   -4
5. 5.

   Kira's bucket-filling chart shows an arithmetic sequence with a(2) = 30 and a(5) = 54. What is a(1)?

   22
6. 6.

   Luz's box-stacking chart shows an arithmetic sequence with a(4) = 50 and a(6) = 80. What is a(1)?

   5
7. 7.

   Milo's kite-string log shows an arithmetic sequence with a(2) = 17 and a(6) = 57. What is a(1)?

   7
8. 8.

   Noah's plant is 10 cm tall at week 0 and grows 3 cm each week. Which formula gives its height h after n weeks?

   • h = 3 + 10n
   • h = 10 + 3(n − 1)
   • h = 10 + 3n
9. 9.

   A science video shows Pia a dish with 200 bacteria at hour 0. The number doubles every hour. Which formula gives the bacteria b after n hours?

   • b = 200 · 2^n
   • b = 200 + 2n
   • b = 200 · 2^(n − 1)
10. 10.

    Tala's game power bar is 120 points at round 0 and keeps 1/2 of its points each round. Which formula gives the points p after n rounds?

    • p = 120 · (1/2)^(n − 1)
    • p = 120 + (1/2)n
    • p = 120 · (1/2)^n