The nth term of an arithmetic progression is \(a_n=7n-3\). Which correctly identifies its first term and common difference?
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Answer and explanation
Correct answer: First term 4 and common difference 7
The standard AP form is \(a_n=a+(n-1)d\). Here, \(a_1=7(1)-3=4\), and each successive term increases by 7, so \(d=7\). The \(-3\) is only a constant term, not the common difference. Exam tip: find \(a_1\) and \(a_2\), then subtract.
Frequently asked questions
What is the correct answer to this question?
First term 4 and common difference 7
Why is this the correct answer?
The standard AP form is \(a_n=a+(n-1)d\). Here, \(a_1=7(1)-3=4\), and each successive term increases by 7, so \(d=7\). The \(-3\) is only a constant term, not the common difference. Exam tip: find \(a_1\) and \(a_2\), then subtract.
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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