What is the (n)th term of the sequence (5,9,17,33,65,\ldots)?
Answer and explanation
Correct answer: (2^{n+1}+1)
Look at the terms by separating a power of 2 from the remaining constant: 5 is \(2^2+1\), 9 is \(2^3+1\), 17 is \(2^4+1\), 33 is \(2^5+1\), and 65 is \(2^6+1\). The exponent starts at 2 when the position is 1, so the exponent in the nth term is \(n+1\). Hence the general term is \(a_n=2^{n+1}+1\).
Checking the formula confirms it: for n=1 it gives \(2^2+1=5\), and for n=5 it gives \(2^6+1=65\). Therefore option A is correct. Option B has the right type of expression but gives 5 for the first term, while option D starts with a different power and gives an incorrect value. Recognizing the doubling pattern and the fixed added 1 is the key step.
Frequently asked questions
What is the correct answer to this question?
(2^{n+1}+1)
Why is this the correct answer?
Look at the terms by separating a power of 2 from the remaining constant: 5 is \(2^2+1\), 9 is \(2^3+1\), 17 is \(2^4+1\), 33 is \(2^5+1\), and 65 is \(2^6+1\). The exponent starts at 2 when the position is 1, so the exponent in the nth term is \(n+1\). Hence the general term is \(a_n=2^{n+1}+1\).
Checking the formula confirms it: for n=1 it gives \(2^2+1=5\), and for n=5 it gives \(2^6+1=65\). Therefore option A is correct. Option B has the right type of expression but gives 5 for the first term, while option D starts with a different power and gives an incorrect value. Recognizing the doubling pattern and the fixed added 1 is the key step.
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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