If (a_6=41) and (a=11), what is (d)?
Answer and explanation
Correct answer: 6
The formula for the nth term of an arithmetic progression is \(a_n=a+(n-1)d\). Therefore, \(a_6=a+5d\). Substituting the given values gives \(41=11+5d\), so \(5d=30\) and \(d=6\). If 5 were chosen, the sixth term would be \(11+5\times5=36\), not 41. Exam tip: the coefficient of \(d\) in \(a_n\) is always \(n-1\), not \(n\).
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The formula for the nth term of an arithmetic progression is \(a_n=a+(n-1)d\). Therefore, \(a_6=a+5d\). Substituting the given values gives \(41=11+5d\), so \(5d=30\) and \(d=6\). If 5 were chosen, the sixth term would be \(11+5\times5=36\), not 41. Exam tip: the coefficient of \(d\) in \(a_n\) is always \(n-1\), not \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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