Sum of a finite geometric series, and infinite geometric series

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. Read this first

   Growth table (round | students | running total)

   1 | 3 | 3; 2 | 6 | 9; 3 | 12 | 21; the rows go on, × 2 on each arrow.

2. 1.

   Luz starts a class message chain: 3 students get it in round 1, and each round twice as many get it. How many students get it in rounds 1 to 6?

   189

3. Growth table (stage | branches | running total)

   1 | 2 | 2; 2 | 6 | 8; 3 | 18 | 26; the rows go on, × 3 on each arrow.

4. 2.

   Milo draws a branching tree with 2 branches at stage 1 and 3 times as many at each new stage. How many branches are drawn in stages 1 to 5?

   242
5. 3.

   Tala uses S = a(1 − rⁿ)/(1 − r) with a = 2, r = 3 and n = 6. What is S?

   728
6. 4.

   Zee uses S = a(1 − rⁿ)/(1 − r) with a = 5, r = 4 and n = 4. What is S?

   425
7. 5.

   Bo uses S = a(1 − rⁿ)/(1 − r) with a = 81, r = 1/3 and n = 4. What is S?

   120
8. 6.

   Esme uses S = a(1 − rⁿ)/(1 − r) with a = 256, r = 1/4 and n = 4. What is S?

   340
9. 7.

   Luz expands Σ from k = 1 to 4 of 2 · 3^(k − 1) on the class board. The expanded row starts with 2 and 6. What is the sum?

   80
10. 8.

    Noah expands Σ from k = 2 to 5 of 3^k on the class board. The expanded row starts with 9 and 27. What is the sum?

    360
11. 9.

    Pia writes the infinite series 9 + 3 + 1 + … on the class board. Which statement about its total is right?

    • Total 13.5, since 9 ÷ (1 − 1/3) = 13.5
    • No total, since the terms never reach 0
    • Total 13, the sum of the terms shown
    • Total 27, since 9 ÷ (1/3) = 27
12. 10.

    Zee writes the infinite series 5 − 5 + 5 − … on the class board. Which statement about its total is right?

    • Total -5, since 5 ÷ (-1) = -5
    • No total, since r = -1 and the total keeps jumping between 5 and 0
    • Total 5, the sum of the terms shown
    • Total 2.5, since 5 ÷ (1 − (-1)) = 2.5