gaokao Mathematics: Sequences and Series

Question 1

In an arithmetic sequence {aₙ}, if a₁ = 3 and the common difference d = 4, what is a₅?

Accepted Answer

19

Answer

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?

Accepted Answer

2

Answer

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, ...

Accepted Answer

155

Answer

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?

Accepted Answer

54

Answer

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?

Accepted Answer

128

Answer

With b₁ = 4 and q = 2, b₆ = 4 × 2⁵ = 4 × 32 = 128.

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