What is the general term of the sequence (1, 8, 27, 64, …)?
Answer and explanation
Correct answer: aₙ = n³
The governing pattern is the sequence of consecutive perfect cubes. The terms can be written as 1³, 2³, 3³, and 4³: 1³ = 1, 2³ = 8, 3³ = 27, and 4³ = 64. Since the nth term is the cube of the position number, the explicit rule is aₙ = n³, making option B correct. Option A gives the square sequence 1, 4, 9, 16, not the given values. Option C produces 3, 6, 9, 12, and option D produces 2, 4, 8, 16 when n begins at 1. Testing the first few positions is sufficient to distinguish the correct rule clearly.
Frequently asked questions
What is the correct answer to this question?
aₙ = n³
Why is this the correct answer?
The governing pattern is the sequence of consecutive perfect cubes. The terms can be written as 1³, 2³, 3³, and 4³: 1³ = 1, 2³ = 8, 3³ = 27, and 4³ = 64. Since the nth term is the cube of the position number, the explicit rule is aₙ = n³, making option B correct. Option A gives the square sequence 1, 4, 9, 16, not the given values. Option C produces 3, 6, 9, 12, and option D produces 2, 4, 8, 16 when n begins at 1. Testing the first few positions is sufficient to distinguish the correct rule clearly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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