What is the nth term of the sequence (1, 8, 27, 64, \ldots)?
Answer and explanation
Correct answer: a_n=n^3
The relevant concept is recognizing the pattern of perfect powers and connecting each term with its position. The displayed values can be written as 1=1^3, 8=2^3, 27=3^3 and 64=4^3. Since the nth term is the cube of n, the explicit rule is a_n=n^3, so option C is correct. Option A gives squares, producing 1, 4, 9, 16. Option B gives powers of 2, producing 2, 4, 8, 16, and option D starts with 8 because it uses (n+1)^3. Checking the first position is especially useful for distinguishing n^3 from (n+1)^3.
Frequently asked questions
What is the correct answer to this question?
a_n=n^3
Why is this the correct answer?
The relevant concept is recognizing the pattern of perfect powers and connecting each term with its position. The displayed values can be written as 1=1^3, 8=2^3, 27=3^3 and 64=4^3. Since the nth term is the cube of n, the explicit rule is a_n=n^3, so option C is correct. Option A gives squares, producing 1, 4, 9, 16. Option B gives powers of 2, producing 2, 4, 8, 16, and option D starts with 8 because it uses (n+1)^3. Checking the first position is especially useful for distinguishing n^3 from (n+1)^3.
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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