What is the general term of the sequence (4,8,16,32,\ldots)?
Answer and explanation
Correct answer: \(a_n=2^{n+1}\)
Each term is twice the preceding term, so this is a geometric sequence. For \(n=1\), \(a_n=2^{n+1}=2^2=4\); for \(n=2\), it gives 8, and for \(n=3\), it gives 16. Hence, the correct general term is \(a_n=2^{n+1}\). Although \(a_n=4n\) gives the first two terms as 4 and 8, its third term is 12, not 16. Exam tip: test a proposed rule using the first two or three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=2^{n+1}\)
Why is this the correct answer?
Each term is twice the preceding term, so this is a geometric sequence. For \(n=1\), \(a_n=2^{n+1}=2^2=4\); for \(n=2\), it gives 8, and for \(n=3\), it gives 16. Hence, the correct general term is \(a_n=2^{n+1}\). Although \(a_n=4n\) gives the first two terms as 4 and 8, its third term is 12, not 16. Exam tip: test a proposed rule using the first two or 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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