Which explicit rule is correct for the sequence (8,20,42,80,\ldots)?
Answer and explanation
Correct answer: \(a_n=3\cdot2^n+2n^2\)
The correct rule is \(a_n=3\cdot2^n+2n^2\). Checking it: for \(n=1\), \(3\cdot2+2=8\); for \(n=2\), \(3\cdot4+8=20\); and for \(n=3\), \(3\cdot8+18=42\). Option C gives the first term \(8\), but for \(n=2\) it gives \(16\), not \(20\). Exam tip: test an explicit rule using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3\cdot2^n+2n^2\)
Why is this the correct answer?
The correct rule is \(a_n=3\cdot2^n+2n^2\). Checking it: for \(n=1\), \(3\cdot2+2=8\); for \(n=2\), \(3\cdot4+8=20\); and for \(n=3\), \(3\cdot8+18=42\). Option C gives the first term \(8\), but for \(n=2\) it gives \(16\), not \(20\). Exam tip: test an explicit rule using at least the first three terms.
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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