Which statement correctly classifies the sequence whose \(n\)th term is \(a_n=5-3n\)?
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Answer and explanation
Correct answer: It is a decreasing AP with common difference \(-3\)
\(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), which is constant for every \(n\). Hence it is an AP; the negative difference makes it decreasing. Exam tip: the coefficient of \(n\) gives the common difference.
Frequently asked questions
What is the correct answer to this question?
It is a decreasing AP with common difference \(-3\)
Why is this the correct answer?
\(a_{n+1}-a_n=[5-3(n+1)]-(5-3n)=-3\), which is constant for every \(n\). Hence it is an AP; the negative difference makes it decreasing. Exam tip: the coefficient of \(n\) gives 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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