Which explicit rule is correct for the sequence (1,16,49,100,\ldots)?
Answer and explanation
Correct answer: \(a_n=(3n-2)^2\)
The terms are \(1^2,4^2,7^2,10^2\). Their square roots, \(1,4,7,10\), form an arithmetic sequence whose \(n\)th term is \(3n-2\). Hence the explicit rule is \(a_n=(3n-2)^2\). In option B, substituting \(n=2\) gives 10, not 16. Exam tip: for sequences of perfect squares, first check the pattern in their square roots.
Frequently asked questions
What is the correct answer to this question?
\(a_n=(3n-2)^2\)
Why is this the correct answer?
The terms are \(1^2,4^2,7^2,10^2\). Their square roots, \(1,4,7,10\), form an arithmetic sequence whose \(n\)th term is \(3n-2\). Hence the explicit rule is \(a_n=(3n-2)^2\). In option B, substituting \(n=2\) gives 10, not 16. Exam tip: for sequences of perfect squares, first check the pattern in their square roots.
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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