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.

   Jun's reading log: 7, 11, 15, 19, … What is the formula for term n? Simplify it.

   4n + 3
2. 2.

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

   9n − 7
3. 3.

   Luz's class counts craft sticks left in a jar: 40, 34, 28, 22, … What is the formula for term n? Simplify it.

   −6n + 46
4. 4.

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

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

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

   4374
6. 6.

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

   122
7. 7.

   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
8. 8.

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

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

   • a(1) = 6, a(n) = a(n − 1) + 2
   • a(1) = 2, a(n) = a(n − 1) + 6
   • a(1) = 8, a(n) = a(n − 1) + 6
10. 10.

    Ren's list has the formula a(n) = 3n − 1. Which recursive rule makes the same list?

    • a(1) = 2, a(n) = a(n − 1) + 3
    • a(1) = 3, a(n) = a(n − 1) − 1
    • a(1) = -1, a(n) = a(n − 1) + 3