Which rule is correct for the sequence (5,25,125,625,\ldots)?
Answer and explanation
Correct answer: \(a_n=5^n\)
The first term is 5, and each successive term is multiplied by 5: \(5,5^2,5^3,5^4,\ldots\). Therefore, when counting starts at \(n=1\), the general term is \(a_n=5^n\). The rule \(a_n=5^{n-1}\) gives 1 as the first term, so it is incorrect. Exam tip: substitute \(n=1\) to check a proposed general rule.
Frequently asked questions
What is the correct answer to this question?
\(a_n=5^n\)
Why is this the correct answer?
The first term is 5, and each successive term is multiplied by 5: \(5,5^2,5^3,5^4,\ldots\). Therefore, when counting starts at \(n=1\), the general term is \(a_n=5^n\). The rule \(a_n=5^{n-1}\) gives 1 as the first term, so it is incorrect. Exam tip: substitute \(n=1\) to check a proposed general rule.
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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