Which explicit rule is correct for the sequence (4, 16, 64, 256, …)?
Answer and explanation
Correct answer: aₙ = 4ⁿ
The sequence is formed by consecutive powers of 4. With the first position numbered n = 1, the terms are 4¹ = 4, 4² = 16, 4³ = 64, and 4⁴ = 256. Hence the explicit rule is aₙ = 4ⁿ, making option C correct. Equivalently, each term is obtained by multiplying the previous term by 4, which is the characteristic pattern of a geometric sequence with first term 4 and common ratio 4. Option A gives 4, 8, 12, 16, while option B gives 1, 16, 81, 256. Option D gives 3, 15, 63, 255. Only option C agrees with every listed position.
Frequently asked questions
What is the correct answer to this question?
aₙ = 4ⁿ
Why is this the correct answer?
The sequence is formed by consecutive powers of 4. With the first position numbered n = 1, the terms are 4¹ = 4, 4² = 16, 4³ = 64, and 4⁴ = 256. Hence the explicit rule is aₙ = 4ⁿ, making option C correct. Equivalently, each term is obtained by multiplying the previous term by 4, which is the characteristic pattern of a geometric sequence with first term 4 and common ratio 4. Option A gives 4, 8, 12, 16, while option B gives 1, 16, 81, 256. Option D gives 3, 15, 63, 255. Only option C agrees with every listed position.
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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