What is the general term of the sequence (10,7,4,1,\ldots)?
Answer and explanation
Correct answer: \(13-3n\)
This is an arithmetic progression with first term \(a=10\) and common difference \(d=7-10=-3\). Therefore, the \(n\)th term is \(a_n=a+(n-1)d=10+(n-1)(-3)=13-3n\). In \(10-3n\), putting \(n=1\) gives 7 rather than the first term 10, so it is incorrect. Exam tip: verify a general term by substituting \(n=1\); it must give the first term.
Frequently asked questions
What is the correct answer to this question?
\(13-3n\)
Why is this the correct answer?
This is an arithmetic progression with first term \(a=10\) and common difference \(d=7-10=-3\). Therefore, the \(n\)th term is \(a_n=a+(n-1)d=10+(n-1)(-3)=13-3n\). In \(10-3n\), putting \(n=1\) gives 7 rather than the first term 10, so it is incorrect. Exam tip: verify a general term by substituting \(n=1\); it must give the first term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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