What is the (n)th term of the sequence (4,12,28,60,124,\ldots)?
Answer and explanation
Correct answer: \(2^{n+2}-4\)
The consecutive terms satisfy \(a_{n+1}=2a_n+4\): \(4\to12\to28\to60\). The corresponding nth term is \(a_n=2^{n+2}-4\). Checking, for \(n=1\), it gives \(8-4=4\), and for \(n=2\), it gives \(16-4=12\). The option \(2^{n+2}+4\) gives 12 as the first term, so it is incorrect. Exam tip: substitute the first two values of \(n\) to check a proposed sequence formula quickly.
Frequently asked questions
What is the correct answer to this question?
\(2^{n+2}-4\)
Why is this the correct answer?
The consecutive terms satisfy \(a_{n+1}=2a_n+4\): \(4\to12\to28\to60\). The corresponding nth term is \(a_n=2^{n+2}-4\). Checking, for \(n=1\), it gives \(8-4=4\), and for \(n=2\), it gives \(16-4=12\). The option \(2^{n+2}+4\) gives 12 as the first term, so it is incorrect. Exam tip: substitute the first two values of \(n\) to check a proposed sequence formula quickly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
