Formulas for the nth term of arithmetic and geometric sequences

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Kira's bike-ride km log: 2, 11, 20, 29, … What is the formula for term n? Simplify it.

   9n − 7
2. 2.

   Noah's sunflower-seed chart: 5, 15, 45, 135, … Which formula gives term n?

   • a(n) = 5 + 10(n − 1)
   • a(n) = 5 · 3^(n − 1)
   • a(n) = 5 · 3^n
   • a(n) = 3 · 5^(n − 1)
3. 3.

   Pia's drum-beat pattern: 2, 8, 32, 128, … Which formula gives term n?

   • a(n) = 2 · 4^(n − 1)
   • a(n) = 2 + 6(n − 1)
   • a(n) = 2 · 4^n
   • a(n) = 4 · 2^(n − 1)
4. 4.

   Tala paints ladder rungs with numbers: 3, 11, 19, 27, … What is term 40?

   315
5. 5.

   Ari's phone game levels give points: 3, 6, 12, 24, … What is term 10?

   1536
6. 6.

   Bo draws branches on a tree picture: 6, 18, 54, 162, … What is term 7?

   4374
7. 7.

   Esme builds a tile pattern. Stage 1 has 5 tiles, and each stage adds 3 tiles. How many tiles does stage 40 have?

   122
8. 8.

   A section of Jun's school theater has 20 seats in row 1, and each row has 2 more. How many seats are in row 12?

   42
9. 9.

   Milo's list has the formula a(n) = 9 + 4(n − 1). Which recursive rule makes the same list?

   • a(1) = 4, a(n) = a(n − 1) + 9
   • a(1) = 9, a(n) = a(n − 1) + 4
   • a(1) = 13, a(n) = a(n − 1) + 4
10. 10.

    Noah's list has the formula a(n) = 6n + 2. Which recursive rule makes the same list?

    • a(1) = 2, a(n) = a(n − 1) + 6
    • a(1) = 8, a(n) = a(n − 1) + 6
    • a(1) = 6, a(n) = a(n − 1) + 2