If (a_n=pn^2+q), (a_1=5) and (a_2=14), what will be (a_4)?
Answer and explanation
Correct answer: 50
Given \(a_n=pn^2+q\), we have \(a_1=p+q=5\) and \(a_2=4p+q=14\). Subtracting the first equation from the second gives \(3p=9\), so \(p=3\) and \(q=2\). Therefore, \(a_4=3\times4^2+2=3\times16+2=50\). Hence, 50 is the correct answer. Although 48 is a close distractor, it does not result from correctly using \(4^2=16\). Exam tip: first find the unknown constants from the given terms, then substitute the required value of \(n\).
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
Given \(a_n=pn^2+q\), we have \(a_1=p+q=5\) and \(a_2=4p+q=14\). Subtracting the first equation from the second gives \(3p=9\), so \(p=3\) and \(q=2\). Therefore, \(a_4=3\times4^2+2=3\times16+2=50\). Hence, 50 is the correct answer. Although 48 is a close distractor, it does not result from correctly using \(4^2=16\). Exam tip: first find the unknown constants from the given terms, then substitute the required value of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
