What is the (n)th term of the sequence (10,21,36,55,78,\ldots)?
Answer and explanation
Correct answer: \(2n^2+5n+3\)
The first differences are \(11,15,19,23\), and the second differences are all \(4\). Hence the sequence has a quadratic nth term, with coefficient of \(n^2\) equal to \(4/2=2\). Let \(a_n=2n^2+bn+c\). Using \(n=1\) and \(n=2\) gives \(b=5\) and \(c=3\), so \(a_n=2n^2+5n+3\). Option B has the same quadratic coefficient but does not fit the second term. Exam tip: for a constant second difference, use a quadratic form for the nth term.
Frequently asked questions
What is the correct answer to this question?
\(2n^2+5n+3\)
Why is this the correct answer?
The first differences are \(11,15,19,23\), and the second differences are all \(4\). Hence the sequence has a quadratic nth term, with coefficient of \(n^2\) equal to \(4/2=2\). Let \(a_n=2n^2+bn+c\). Using \(n=1\) and \(n=2\) gives \(b=5\) and \(c=3\), so \(a_n=2n^2+5n+3\). Option B has the same quadratic coefficient but does not fit the second term. Exam tip: for a constant second difference, use a quadratic form for the nth term.
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.
