What is the general term of the sequence (1,15,63,195,\ldots)?
Answer and explanation
Correct answer: The general term cannot be determined uniquely from the given finite information.
With only four given terms, the general term of a sequence is not uniquely determined. For example, the polynomial in option C gives \(1,15,63,195\) for \(n=1,2,3,4\), but many other rules can also produce these same four terms. Option A fits only the first two terms; at \(n=3\), it gives \(53\), not \(63\). Exam tip: Test a proposed rule against every listed term and check whether enough information is available to define a unique pattern.
Frequently asked questions
What is the correct answer to this question?
The general term cannot be determined uniquely from the given finite information.
Why is this the correct answer?
With only four given terms, the general term of a sequence is not uniquely determined. For example, the polynomial in option C gives \(1,15,63,195\) for \(n=1,2,3,4\), but many other rules can also produce these same four terms. Option A fits only the first two terms; at \(n=3\), it gives \(53\), not \(63\). Exam tip: Test a proposed rule against every listed term and check whether enough information is available to define a unique pattern.
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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