For an arithmetic progression with (a=12) and (a_7=54), what is (d)?
Answer and explanation
Correct answer: 7
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Hence, \(a_7=12+(7-1)d=12+6d\). So, \(54=12+6d\), giving \(6d=42\) and \(d=7\). If \(d=6\), the seventh term would be \(12+6\times6=48\), not 54. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The formula for an arithmetic progression is \(a_n=a+(n-1)d\). Hence, \(a_7=12+(7-1)d=12+6d\). So, \(54=12+6d\), giving \(6d=42\) and \(d=7\). If \(d=6\), the seventh term would be \(12+6\times6=48\), not 54. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
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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