What is the nth term of the sequence 27, 64, 125, 216, …?
Answer and explanation
Correct answer: aₙ = (n + 2)³
The governing concept is identifying an explicit nth-term rule by recognizing perfect cubes and matching their positions. The terms are 27 = 3³, 64 = 4³, 125 = 5³, and 216 = 6³. The cube bases therefore begin at 3 when the position is n = 1, and increase by one as n increases. The base can be written as n + 2, so the general term is aₙ = (n + 2)³. Checking confirms that n = 1 gives 3³ = 27 and n = 4 gives 6³ = 216. Option A would start with 1, option B with 2, and option D does not preserve the cube pattern. Thus C is correct.
Frequently asked questions
What is the correct answer to this question?
aₙ = (n + 2)³
Why is this the correct answer?
The governing concept is identifying an explicit nth-term rule by recognizing perfect cubes and matching their positions. The terms are 27 = 3³, 64 = 4³, 125 = 5³, and 216 = 6³. The cube bases therefore begin at 3 when the position is n = 1, and increase by one as n increases. The base can be written as n + 2, so the general term is aₙ = (n + 2)³. Checking confirms that n = 1 gives 3³ = 27 and n = 4 gives 6³ = 216. Option A would start with 1, option B with 2, and option D does not preserve the cube pattern. Thus C is correct.
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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