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.

   Milo tracks mL of juice left, in tens: 25, 21, 17, 13, … What is the formula for term n? Simplify it.

   −4n + 29
4. 4.

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

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

   315
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.

   Luz keeps cutting paper in half and stacking the halves. After step 1 the stack is 0.2 mm thick; each step doubles it (× 2). How many mm thick is it after step 8?

   25.6
9. 9.

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

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

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