The nth term of an arithmetic progression is given by \(a_n=12-3(n-1)\). Which correctly identifies the first term and the common difference of this AP?
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Answer and explanation
Correct answer: First term 12, common difference −3
The standard form is \(a_n=a+(n-1)d\). Comparing it with \(12-3(n-1)\) gives \(a=12\) and \(d=-3\). The negative difference means each next term decreases by 3. Exam tip: carefully retain the sign of the coefficient of \((n-1)\).
Frequently asked questions
What is the correct answer to this question?
First term 12, common difference −3
Why is this the correct answer?
The standard form is \(a_n=a+(n-1)d\). Comparing it with \(12-3(n-1)\) gives \(a=12\) and \(d=-3\). The negative difference means each next term decreases by 3. Exam tip: carefully retain the sign of the coefficient of \((n-1)\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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