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.

   Ren measures a play ball's bounces in cm: 120, 60, 30, 15, … Which formula gives term n?

   • a(n) = 120 · (1/2)^n
   • a(n) = 120 · (1/2)^(n − 1)
   • a(n) = (1/2) · 120^(n − 1)
   • a(n) = 120 − 60(n − 1)
3. 3.

   Zee's minutes left in a countdown: 60, 55, 50, 45, … What is term 12?

   5
4. 4.

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

   122
5. 5.

   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
6. 6.

   In round 1 of Kira's school phone tree, 6 parents hear the news. Each round, 3 times as many hear it. How many hear it in round 4?

   162
7. 7.

   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
8. 8.

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

   Pia's list has the formula a(n) = 2 · 5^(n − 1). Which recursive rule makes the same list?

   • a(1) = 2, a(n) = 5 · a(n − 1)
   • a(1) = 5, a(n) = 2 · a(n − 1)
   • a(1) = 10, a(n) = 5 · a(n − 1)
10. 10.

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

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