Sequences and Series Quiz

Grade 11 · Math · Quiz

10 questions on arithmetic and geometric sequences, partial sums, and infinite series.

Questions

1. What is the common difference in the arithmetic sequence 12, 9, 6, 3, …?

   1. 3
   2. −3
   3. 4
   4. −4
   Show answer

   Answer: −3

   Each term decreases by 3, so d = −3.

2. Find a₆ for the geometric sequence with a₁ = 3 and r = 2.

   1. 48
   2. 96
   3. 64
   4. 192
   Show answer

   Answer: 96

   a₆ = 3 · 2⁵ = 3 · 32 = 96.

3. What is the sum of the first 5 terms of the arithmetic series 1 + 4 + 7 + 10 + 13?

   1. 30
   2. 35
   3. 25
   4. 40
   Show answer

   Answer: 35

   S₅ = 5(1+13)/2 = 5·14/2 = 35.

4. What is the sum of the infinite geometric series 9 + 3 + 1 + 1/3 + …?

   1. 13.5
   2. 27/2
   3. 12
   4. 27
   Show answer

   Answer: 27/2

   r = 1/3, S = 9/(1−1/3) = 9/(2/3) = 27/2 = 13.5.

5. Which sequence is geometric: 2, 4, 8, 16 or 2, 5, 8, 11?

   1. 2, 5, 8, 11
   2. 2, 4, 8, 16
   3. Both
   4. Neither
   Show answer

   Answer: 2, 4, 8, 16

   2, 4, 8, 16 has constant ratio r=2. The other has constant difference d=3 (arithmetic).

6. Evaluate Σᵢ₌₁³ i².

   1. 9
   2. 14
   3. 6
   4. 16
   Show answer

   Answer: 14

   1² + 2² + 3² = 1 + 4 + 9 = 14.

7. Does the series 5 + 10 + 20 + 40 + … converge?

   1. Yes, to 10
   2. Yes, to 100
   3. No, it diverges
   4. Yes, to 5
   Show answer

   Answer: No, it diverges

   r = 2, |r| = 2 ≥ 1, so the series diverges.

8. Find the 15th term of the arithmetic sequence with a₁ = 10 and d = −2.

   1. −18
   2. −16
   3. 38
   4. −20
   Show answer

   Answer: −18

   a₁₅ = 10 + (15−1)(−2) = 10 − 28 = −18.

9. What is the 4th partial sum S₄ for the geometric series with a₁ = 1 and r = 3?

   1. 13
   2. 40
   3. 27
   4. 26
   Show answer

   Answer: 40

   1 + 3 + 9 + 27 = 40. Or S₄ = 1·(1−3⁴)/(1−3) = (1−81)/(−2) = 80/2 = 40.

10. A geometric series has a₁ = 100 and r = 0.5. What is S∞?

    1. 50
    2. 100
    3. 200
    4. 150
    Show answer

    Answer: 200

    S∞ = 100/(1−0.5) = 100/0.5 = 200.

Get a personalized course on Sequences and Series built around your child.