The nth term of an arithmetic progression is \(a_n=7n-3\). Which of the following statements must be true?
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Answer and explanation
Correct answer: The first term is 4 and the common difference is 7
For an AP, \(a_n=a+(n-1)d=dn+(a-d)\). Comparing with \(7n-3\) gives \(d=7\) and \(a-d=-3\), so \(a=4\). Option B wrongly treats −3 as the first term. Exam tip: in linear nth-term form, the coefficient of \(n\) is the common difference.
Frequently asked questions
What is the correct answer to this question?
The first term is 4 and the common difference is 7
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d=dn+(a-d)\). Comparing with \(7n-3\) gives \(d=7\) and \(a-d=-3\), so \(a=4\). Option B wrongly treats −3 as the first term. Exam tip: in linear nth-term form, the coefficient of \(n\) is the common difference.
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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