Which is the (n)th term of the sequence (7,11,19,35,67,\ldots)?
Answer and explanation
Correct answer: \(2^{n+1}+3\)
The consecutive differences are \(4,8,16,32\), and each difference doubles. Substituting \(n=1,2,3\) in \(2^{n+1}+3\) gives \(7,11,19\), so it matches the sequence. Although \(2^n+5\) gives the first term, it gives \(9\) when \(n=2\), so it is incorrect. Exam tip: for an exponential sequence, first inspect the pattern of consecutive differences.
Frequently asked questions
What is the correct answer to this question?
\(2^{n+1}+3\)
Why is this the correct answer?
The consecutive differences are \(4,8,16,32\), and each difference doubles. Substituting \(n=1,2,3\) in \(2^{n+1}+3\) gives \(7,11,19\), so it matches the sequence. Although \(2^n+5\) gives the first term, it gives \(9\) when \(n=2\), so it is incorrect. Exam tip: for an exponential sequence, first inspect the pattern of consecutive differences.
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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