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. Growth table (stage | squares | running total)

   1 | 1 | 1; 2 | 4 | 5; 3 | 16 | 21; the rows go on, × 4 on each arrow.

6. 3.

   Pia draws a square pattern: stage 1 has 1 square, and each stage has 4 times as many. How many squares are in stages 1 to 5 together?

   341
7. 4.

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

   728
8. 5.

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

   425
9. 6.

   Jun expands Σ from k = 1 to 5 of 3 · 2^(k − 1) on the class board. The expanded row starts with 3 and 6. What is the sum?

   93
10. 7.

    Milo expands Σ from k = 0 to 5 of 5 · 2^k on the class board. The expanded row starts with 5 and 10. What is the sum?

    315
11. 8.

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

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

    Ren writes the infinite series 16 + 4 + 1 + … on the class board. Which statement about its total is right?

    • No total, since the terms never reach 0
    • Total 21, the sum of the terms shown
    • Total 64, since 16 ÷ (1/4) = 64
    • Total 64/3, since 16 ÷ (1 − 1/4) = 64/3
13. 10.

    Tala writes the infinite series 2 + 6 + 18 + … on the class board. Which statement about its total is right?

    • Total 2/3, since 2 ÷ 3 = 2/3
    • Total 26, the sum of the terms shown on the class board
    • Total -1, since 2 ÷ (1 − 3) = -1
    • No total, since r = 3 and the terms keep growing