What is the general term of the sequence (1, 4, 9, 16, …)?
Answer and explanation
Correct answer: a_n = n^2
The governing pattern is the sequence of consecutive square numbers. The terms can be written as 1^2, 2^2, 3^2, and 4^2. Since the term in position n is the square of n, its explicit rule is a_n = n^2, making option C correct. Substitution verifies the rule: for n = 1, a_1 = 1; for n = 2, a_2 = 4; for n = 3, a_3 = 9; and for n = 4, a_4 = 16. Option A produces 2, 3, 4, 5, option B produces even numbers, and option D produces multiples of 3. Although the differences between the terms are 3, 5, and 7 rather than constant, the square-number rule identifies the sequence directly.
Frequently asked questions
What is the correct answer to this question?
a_n = n^2
Why is this the correct answer?
The governing pattern is the sequence of consecutive square numbers. The terms can be written as 1^2, 2^2, 3^2, and 4^2. Since the term in position n is the square of n, its explicit rule is a_n = n^2, making option C correct. Substitution verifies the rule: for n = 1, a_1 = 1; for n = 2, a_2 = 4; for n = 3, a_3 = 9; and for n = 4, a_4 = 16. Option A produces 2, 3, 4, 5, option B produces even numbers, and option D produces multiples of 3. Although the differences between the terms are 3, 5, and 7 rather than constant, the square-number rule identifies the sequence directly.
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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