What is the general term of the sequence (8, 27, 64, 125, ...)?
Answer and explanation
Correct answer: aₙ = (n + 1)³
The governing concept is an explicit or general rule: a formula must produce the term directly from its position n. Rewrite the sequence as 2³, 3³, 4³, 5³, ... . The first displayed term corresponds to n = 1, so its cube base is n + 1; therefore the rule is aₙ = (n + 1)³. Checking confirms it: for n = 1, a₁ = 2³ = 8; for n = 2, a₂ = 3³ = 27; for n = 3, a₃ = 4³ = 64; and for n = 4, a₄ = 5³ = 125. Thus option B is correct. Option A starts with 1³, option C gives 2 at n = 1, and option D starts with 3³, so those alternatives do not match the sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = (n + 1)³
Why is this the correct answer?
The governing concept is an explicit or general rule: a formula must produce the term directly from its position n. Rewrite the sequence as 2³, 3³, 4³, 5³, ... . The first displayed term corresponds to n = 1, so its cube base is n + 1; therefore the rule is aₙ = (n + 1)³. Checking confirms it: for n = 1, a₁ = 2³ = 8; for n = 2, a₂ = 3³ = 27; for n = 3, a₃ = 4³ = 64; and for n = 4, a₄ = 5³ = 125. Thus option B is correct. Option A starts with 1³, option C gives 2 at n = 1, and option D starts with 3³, so those alternatives do not match the sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
