Which is the (n)th term of the sequence (2,6,14,30,62,\ldots)?
Answer and explanation
Correct answer: \(2^{n+1}-2\)
The terms can be written as \(4-2, 8-2, 16-2, 32-2, 64-2\). The subtracted value is always \(2\), and the nth term of \(4,8,16,32,64\) is \(2^{n+1}\). Hence, the nth term is \(2^{n+1}-2\). Option \(2^{n+2}-6\) gives the first term correctly, but for \(n=2\) it gives \(10\), not \(6\). Exam tip: verify a proposed nth-term formula by substituting \(n=1\) and \(n=2\).
Frequently asked questions
What is the correct answer to this question?
\(2^{n+1}-2\)
Why is this the correct answer?
The terms can be written as \(4-2, 8-2, 16-2, 32-2, 64-2\). The subtracted value is always \(2\), and the nth term of \(4,8,16,32,64\) is \(2^{n+1}\). Hence, the nth term is \(2^{n+1}-2\). Option \(2^{n+2}-6\) gives the first term correctly, but for \(n=2\) it gives \(10\), not \(6\). Exam tip: verify a proposed nth-term formula by substituting \(n=1\) and \(n=2\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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