If (a=7) and (a_{11}=67), what is (d)?
Answer and explanation
Correct answer: \(6\)
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Substituting \(a=7\), \(n=11\), and \(a_{11}=67\) gives \(67=7+10d\). Hence, \(10d=60\), so \(d=6\). If \(d=5\), the eleventh term would be \(57\), so it is not correct. Exam tip: the coefficient of \(d\) in the \(n\)th-term formula is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
\(6\)
Why is this the correct answer?
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Substituting \(a=7\), \(n=11\), and \(a_{11}=67\) gives \(67=7+10d\). Hence, \(10d=60\), so \(d=6\). If \(d=5\), the eleventh term would be \(57\), so it is not correct. Exam tip: the coefficient of \(d\) in the \(n\)th-term formula 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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