What is the nth term of the sequence 8, 27, 64, 125, …?
Answer and explanation
Correct answer: (n + 1)³
The governing concept is identifying a pattern and expressing it as a general term. The given numbers are consecutive cubes: 8 = 2³, 27 = 3³, 64 = 4³, and 125 = 5³. Since the first term corresponds to base 2 rather than base 1, the base for the nth term is n + 1. Thus aₙ = (n + 1)³, so option A is correct. The rule can be verified at more than one position: for n = 1, it gives (1 + 1)³ = 8; for n = 2, it gives 3³ = 27; and for n = 4, it gives 5³ = 125. Option B is not equivalent to the correct expression because expanding the latter gives n³ + 3n² + 3n + 1. Options C and D also fail these checks.
Frequently asked questions
What is the correct answer to this question?
(n + 1)³
Why is this the correct answer?
The governing concept is identifying a pattern and expressing it as a general term. The given numbers are consecutive cubes: 8 = 2³, 27 = 3³, 64 = 4³, and 125 = 5³. Since the first term corresponds to base 2 rather than base 1, the base for the nth term is n + 1. Thus aₙ = (n + 1)³, so option A is correct. The rule can be verified at more than one position: for n = 1, it gives (1 + 1)³ = 8; for n = 2, it gives 3³ = 27; and for n = 4, it gives 5³ = 125. Option B is not equivalent to the correct expression because expanding the latter gives n³ + 3n² + 3n + 1. Options C and D also fail these checks.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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