Formulas for the nth term of arithmetic and geometric sequences

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Jun's pencil-count pattern has a formula. The formula is a(n) = 7 + 4(n − 1). What is a(20)?

   83
2. 2.

   Kira's block tower pattern has a formula. The formula is a(n) = 12 + 5(n − 1). What is a(30)?

   157
3. 3.

   Luz's countdown timer pattern has a formula. The formula is a(n) = 50 − 3(n − 1). What is a(11)?

   20
4. 4.

   Milo's paper-cutting pattern has a formula. The formula is a(n) = 3 · 2^(n − 1). What is a(6)?

   96
5. 5.

   Noah's star pattern has a formula. The formula is a(n) = 5 · 3^(n − 1). What is a(4)?

   135
6. 6.

   Pia's flower pattern has a formula. The formula is a(n) = 4 · 5^(n − 1). What is a(3)?

   100
7. 7.

   1 | 9; 2 | 15; 3 | 21; … Every arrow: + 6. Ren sets out chairs in a growing pattern. Term 1 is 9 and every arrow is + 6. Term 25 is 24 arrows after term 1. What is term 25?

   153
8. 8.

   1 | 15; 2 | 19; 3 | 23; … Every arrow: + 4. Tala lines up crayons in a growing pattern. Term 1 is 15 and every arrow is + 4. Term 40 is 39 arrows after term 1. What is term 40?

   171
9. 9.

   1 | 100; 2 | 93; 3 | 86; … Every arrow: − 7. Zee's water tank drains in steady steps. Term 1 is 100 and every arrow is − 7. Term 13 is 12 arrows after term 1. What is term 13?

   16
10. 10.

    1 | 7; 2 | 21; 3 | 63; … Every arrow: × 3. Esme's leaf-pattern drawing grows. Term 1 is 7 and every arrow is × 3. Term 5 is 4 arrows after term 1. What is term 5?

    567