Sum of a finite geometric series, and infinite geometric series
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
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.
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?
Growth table (stage | branches | running total)
1 | 2 | 2; 2 | 6 | 8; 3 | 18 | 26; the rows go on, × 3 on each arrow.
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?
Tala uses S = a(1 − rⁿ)/(1 − r) with a = 2, r = 3 and n = 6. What is S?
Zee uses S = a(1 − rⁿ)/(1 − r) with a = 5, r = 4 and n = 4. What is S?
Bo uses S = a(1 − rⁿ)/(1 − r) with a = 81, r = 1/3 and n = 4. What is S?
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?
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?
Pia writes the infinite series 9 + 3 + 1 + … on the class board. Which statement about its total is right?
- Total 13, the sum of the terms shown
- Total 13.5, since 9 ÷ (1 − 1/3) = 13.5
- No total, since the terms never reach 0
- Total 27, since 9 ÷ (1/3) = 27
Ren writes the infinite series 16 + 4 + 1 + … on the class board. Which statement about its total is right?
- Total 64, since 16 ÷ (1/4) = 64
- Total 64/3, since 16 ÷ (1 − 1/4) = 64/3
- Total 21, the sum of the terms shown
- No total, since the terms never reach 0
Tala writes the infinite series 2 + 6 + 18 + … on the class board. Which statement about its total is right?
- Total -1, since 2 ÷ (1 − 3) = -1
- Total 2/3, since 2 ÷ 3 = 2/3
- No total, since r = 3 and the terms keep growing
- Total 26, the sum of the terms shown on the class board