What is the general term of the sequence (9, 49, 121, 225, ...)?
Answer and explanation
Correct answer: a_n = (4n - 1)^2
The governing concept is finding an explicit rule by identifying a pattern in the terms. Each term is a square: 9 = 3^2, 49 = 7^2, 121 = 11^2, and 225 = 15^2. The bases 3, 7, 11, 15 form an arithmetic sequence with first term 3 and common difference 4. Therefore, the nth base is 3 + 4(n - 1) = 4n - 1, so the nth term is a_n = (4n - 1)^2. Substitution confirms the rule: n = 1 gives 9 and n = 2 gives 49. Option B produces 9, 25, 49, so it does not match; C and D also fail at the second term. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
a_n = (4n - 1)^2
Why is this the correct answer?
The governing concept is finding an explicit rule by identifying a pattern in the terms. Each term is a square: 9 = 3^2, 49 = 7^2, 121 = 11^2, and 225 = 15^2. The bases 3, 7, 11, 15 form an arithmetic sequence with first term 3 and common difference 4. Therefore, the nth base is 3 + 4(n - 1) = 4n - 1, so the nth term is a_n = (4n - 1)^2. Substitution confirms the rule: n = 1 gives 9 and n = 2 gives 49. Option B produces 9, 25, 49, so it does not match; C and D also fail at the second term. Hence option A 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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