If (a_n=2n^2+kn+3) and (a_3=30), what will be the value of (a_5)?
Answer and explanation
Correct answer: 68
Given \(a_n=2n^2+kn+3\), put \(n=3\): \(a_3=2(3)^2+3k+3=21+3k\). Since \(a_3=30\), \(21+3k=30\), so \(k=3\). Now put \(n=5\): \(a_5=2(5)^2+3(5)+3=50+15+3=68\). Hence, 68 is correct. A value such as 72 may result from using an incorrect value of \(k\) or making an addition error. Exam tip: first use the given term to find the unknown constant, then substitute the required value of \(n\).
Frequently asked questions
What is the correct answer to this question?
68
Why is this the correct answer?
Given \(a_n=2n^2+kn+3\), put \(n=3\): \(a_3=2(3)^2+3k+3=21+3k\). Since \(a_3=30\), \(21+3k=30\), so \(k=3\). Now put \(n=5\): \(a_5=2(5)^2+3(5)+3=50+15+3=68\). Hence, 68 is correct. A value such as 72 may result from using an incorrect value of \(k\) or making an addition error. Exam tip: first use the given term to find the unknown constant, 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: nth term.
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