If the nth term of a sequence is \(a_n=7n+4\), what type of sequence is it?
Answer and explanation
Correct answer: An arithmetic progression with common difference 7
Find the difference between consecutive terms: \(a_{n+1}-a_n=[7(n+1)+4]-(7n+4)=7\). Since this difference is constant, the sequence is an arithmetic progression with common difference 7. It is not a geometric progression because the ratio of consecutive terms is not constant. Exam tip: for a sequence of the form \(a_n=pn+q\), the common difference is \(p\).
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What is the correct answer to this question?
An arithmetic progression with common difference 7
Why is this the correct answer?
Find the difference between consecutive terms: \(a_{n+1}-a_n=[7(n+1)+4]-(7n+4)=7\). Since this difference is constant, the sequence is an arithmetic progression with common difference 7. It is not a geometric progression because the ratio of consecutive terms is not constant. Exam tip: for a sequence of the form \(a_n=pn+q\), the common difference is \(p\).
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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