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.

   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
2. 2.

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

   −4n + 29
3. 3.

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

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

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

   • a(n) = 120 − 60(n − 1)
   • a(n) = 120 · (1/2)^n
   • a(n) = 120 · (1/2)^(n − 1)
   • a(n) = (1/2) · 120^(n − 1)
5. 5.

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

   315
6. 6.

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

   5
7. 7.

   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
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.

   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
10. 10.

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

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