If (a_n=an^2+bn+1), (a_1=6), and (a_2=17), what will be (a_5)?
Answer and explanation
Correct answer: 86
Given \(a_n=an^2+bn+1\), putting \(n=1\) gives \(a+b+1=6\), so \(a+b=5\). Putting \(n=2\) gives \(4a+2b+1=17\), so \(2a+b=8\). Solving these equations gives \(a=3\) and \(b=2\). Hence, \(a_5=3(5)^2+2(5)+1=75+10+1=86\). Option 84 would result from omitting the constant term \(+1\). Exam tip: substitute the given term numbers first to form linear equations for the unknown coefficients.
Frequently asked questions
What is the correct answer to this question?
86
Why is this the correct answer?
Given \(a_n=an^2+bn+1\), putting \(n=1\) gives \(a+b+1=6\), so \(a+b=5\). Putting \(n=2\) gives \(4a+2b+1=17\), so \(2a+b=8\). Solving these equations gives \(a=3\) and \(b=2\). Hence, \(a_5=3(5)^2+2(5)+1=75+10+1=86\). Option 84 would result from omitting the constant term \(+1\). Exam tip: substitute the given term numbers first to form linear equations for the unknown coefficients.
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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