If the nth term of a sequence is \(a_n=7n+1\), which statement about it is correct?
Answer and explanation
Correct answer: It is an arithmetic progression with common difference 7.
For consecutive terms, \(a_{n+1}-a_n=[7(n+1)+1]-(7n+1)=7\). Since this difference is constant, the sequence is an arithmetic progression with common difference 7. Option B is incorrect because a geometric progression must have a constant ratio between consecutive terms. Exam tip: for a sequence of the form \(a_n=dn+c\), \(d\) is the common difference.
Frequently asked questions
What is the correct answer to this question?
It is an arithmetic progression with common difference 7.
Why is this the correct answer?
For consecutive terms, \(a_{n+1}-a_n=[7(n+1)+1]-(7n+1)=7\). Since this difference is constant, the sequence is an arithmetic progression with common difference 7. Option B is incorrect because a geometric progression must have a constant ratio between consecutive terms. Exam tip: for a sequence of the form \(a_n=dn+c\), \(d\) is the common difference.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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