Which is the (n)th term of the sequence (1,6,15,28,45,\ldots)?
Answer and explanation
Correct answer: \(n(2n-1)\)
The successive differences are \(5,9,13,17\), and their differences are constantly \(4\). Hence the nth term should be a quadratic expression in \(n\). With \(a_n=n(2n-1)=2n^2-n\), we get \(a_1=1\), \(a_2=6\), \(a_3=15\), \(a_4=28\), and \(a_5=45\). Therefore, option D is correct. Option C gives \(3\) when \(n=1\), so it cannot represent the sequence. Exam tip: a constant second difference usually indicates a quadratic nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(n(2n-1)\)
Why is this the correct answer?
The successive differences are \(5,9,13,17\), and their differences are constantly \(4\). Hence the nth term should be a quadratic expression in \(n\). With \(a_n=n(2n-1)=2n^2-n\), we get \(a_1=1\), \(a_2=6\), \(a_3=15\), \(a_4=28\), and \(a_5=45\). Therefore, option D is correct. Option C gives \(3\) when \(n=1\), so it cannot represent the sequence. Exam tip: a constant second difference usually indicates a quadratic nth-term formula.
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.
