If the common difference is (0), what type of arithmetic progression is formed?
Answer and explanation
Correct answer: All terms are equal
The general term of an arithmetic progression is \(a_n=a_1+(n-1)d\). When the common difference is \(d=0\), we get \(a_n=a_1\), so every term is equal to the first term and all terms are equal. All terms will be zero only if the first term is also zero. Exam tip: Recognise an AP with \(d=0\) as a constant sequence.
Frequently asked questions
What is the correct answer to this question?
All terms are equal
Why is this the correct answer?
The general term of an arithmetic progression is \(a_n=a_1+(n-1)d\). When the common difference is \(d=0\), we get \(a_n=a_1\), so every term is equal to the first term and all terms are equal. All terms will be zero only if the first term is also zero. Exam tip: Recognise an AP with \(d=0\) as a constant sequence.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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