If (a=2) and (a_9=50), what is (d)?
Answer and explanation
Correct answer: 6
For an arithmetic progression, \(a_n=a+(n-1)d\). Hence, \(a_9=2+(9-1)d=2+8d\). Given \(a_9=50\), we get \(50=2+8d\), so \(8d=48\) and \(d=6\). If \(d=5\), the ninth term would be \(2+8\times5=42\), not 50. Exam tip: in the \(n\)th-term formula, the coefficient of \(d\) is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For an arithmetic progression, \(a_n=a+(n-1)d\). Hence, \(a_9=2+(9-1)d=2+8d\). Given \(a_9=50\), we get \(50=2+8d\), so \(8d=48\) and \(d=6\). If \(d=5\), the ninth term would be \(2+8\times5=42\), not 50. Exam tip: in the \(n\)th-term formula, the coefficient of \(d\) is always \(n-1\).
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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