gaokao Mathematics: Sequences and Series 1 — Questions and Answers
Question 1: In an arithmetic sequence {aₙ}, if a₁ = 3 and the common difference d = 4, what is a₅?
- 15
- 19 (Correct answer)
- 17
- 16
Correct answer: 19
Using the formula aₙ = a₁ + (n−1)d, a₅ = 3 + (5−1)×4 = 3 + 16 = 19.
Question 2: The nth term of an arithmetic sequence is given by aₙ = 2n + 1. What is the common difference?
- 1
- 3
- 2 (Correct answer)
- 4
Correct answer: 2
The common difference equals the coefficient of n in the linear formula aₙ = dn + c, so d = 2.
Question 3: Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ...
- 145
- 155 (Correct answer)
- 165
- 175
Correct answer: 155
With a₁ = 2, d = 3, a₁₀ = 2 + 9×3 = 29; S₁₀ = 10(2 + 29)/2 = 5 × 31 = 155.
Question 4: In a geometric sequence {bₙ}, b₁ = 2 and common ratio q = 3. What is b₄?
- 54 (Correct answer)
- 162
- 18
- 81
Correct answer: 54
Using bₙ = b₁ × q^(n−1), b₄ = 2 × 3³ = 2 × 27 = 54.
Question 5: The first three terms of a geometric sequence are 4, 8, 16. What is b₆?
- 64
- 128 (Correct answer)
- 256
- 512
Correct answer: 128
With b₁ = 4 and q = 2, b₆ = 4 × 2⁵ = 4 × 32 = 128.
Question 6: Find the sum of the first 5 terms of the geometric sequence with b₁ = 1 and q = 2.
- 31 (Correct answer)
- 15
- 63
- 32
Correct answer: 31
Using Sₙ = b₁(qⁿ − 1)/(q − 1), S₅ = 1(2⁵ − 1)/(2 − 1) = 32 − 1 = 31.
Question 7: For the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ..., what is the sum?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
For an infinite geometric series with |q| < 1, S = a₁/(1 − q) = 1/(1 − 1/2) = 1/(1/2) = 2.
gaokao Mathematics: Sequences and Series 1
In an arithmetic sequence {aₙ}, if a₁ = 3 and the common difference d = 4, what is a₅?