Sequences and Series Quiz

Grade 9 · Math · Quiz

Evaluate your knowledge of arithmetic and geometric sequences, formulas, and series summation.

Questions

1. What is the common difference in the arithmetic sequence: −3, 1, 5, 9, ...?

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

   Answer: 4

   d = 1 − (−3) = 4. Check: 5 − 1 = 4, 9 − 5 = 4. Confirmed d = 4.

2. Find the 8th term of the arithmetic sequence with a₁ = 7 and d = −3.

   1. −14
   2. −28
   3. −14
   4. 28
   Show answer

   Answer: −14

   a₈ = 7 + (8−1)(−3) = 7 + (−21) = −14.

3. A geometric sequence has a₁ = 2 and r = 3. What is a₄?

   1. 18
   2. 54
   3. 24
   4. 162
   Show answer

   Answer: 54

   a₄ = 2 · 3^(4−1) = 2 · 27 = 54.

4. Find the sum of the first 5 terms of the geometric series: 1 + 2 + 4 + 8 + ...

   1. 15
   2. 31
   3. 16
   4. 32
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   Answer: 31

   S₅ = 1 · (1 − 2⁵)/(1 − 2) = (1 − 32)/(−1) = (−31)/(−1) = 31.

5. Which recursive formula correctly defines the arithmetic sequence 10, 7, 4, 1, ...?

   1. aₙ = aₙ₋₁ + 3
   2. aₙ = aₙ₋₁ − 3
   3. aₙ = 3 · aₙ₋₁
   4. aₙ = aₙ₋₁ ÷ 3
   Show answer

   Answer: aₙ = aₙ₋₁ − 3

   Each term decreases by 3, so the recursive formula is aₙ = aₙ₋₁ − 3.

6. The sum of the first n terms of an arithmetic series is 120, with a₁ = 3 and aₙ = 21. Find n.

   1. 8
   2. 10
   3. 12
   4. 6
   Show answer

   Answer: 10

   Sₙ = n/2 · (a₁ + aₙ). 120 = n/2 · (3 + 21) = 12n. n = 120/12 = 10.

7. In a geometric sequence where r = 1/2 and a₁ = 64, the fourth term is 8.

   Show answer

   Answer: True

   a₄ = 64 · (1/2)³ = 64 · 1/8 = 8. Confirmed.

8. Write the explicit formula for the arithmetic sequence 6, 11, 16, 21, ... The formula is aₙ = 5n + __.

   Show answer

   Answer: 1

   aₙ = a₁ + (n−1)·d = 6 + (n−1)·5 = 6 + 5n − 5 = 5n + 1. Verify: a₁ = 5(1)+1 = 6 ✓

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