Which is the (n)th term of the sequence (7,10,15,22,31,\ldots)?
Answer and explanation
Correct answer: \(n^2+6\)
Check the terms: \(7=1^2+6\), \(10=2^2+6\), \(15=3^2+6\), \(22=4^2+6\), and \(31=5^2+6\). Therefore, the \(n\)th term is \(n^2+6\). The expression \(2n+5\) is linear, so it would have a constant first difference, whereas this sequence has differences \(3,5,7,9\). Exam tip: If first differences are consecutive odd numbers, test a rule involving \(n^2\).
Frequently asked questions
What is the correct answer to this question?
\(n^2+6\)
Why is this the correct answer?
Check the terms: \(7=1^2+6\), \(10=2^2+6\), \(15=3^2+6\), \(22=4^2+6\), and \(31=5^2+6\). Therefore, the \(n\)th term is \(n^2+6\). The expression \(2n+5\) is linear, so it would have a constant first difference, whereas this sequence has differences \(3,5,7,9\). Exam tip: If first differences are consecutive odd numbers, test a rule involving \(n^2\).
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.
