The sequence (18, 18-c, 18-3c) is an arithmetic progression. What is the correct conclusion about (c)?
Answer and explanation
Correct answer: \(c=0\)
In an arithmetic progression, consecutive differences must be equal. Here, second term − first term is \((18-c)-18=-c\), while third term − second term is \((18-3c)-(18-c)=-2c\). Therefore, \(-c=-2c\), which gives \(c=0\). For \(c=1\) or \(c=3\), the two differences are not equal. Exam tip: For three terms to be in AP, equate their two consecutive differences.
Frequently asked questions
What is the correct answer to this question?
\(c=0\)
Why is this the correct answer?
In an arithmetic progression, consecutive differences must be equal. Here, second term − first term is \((18-c)-18=-c\), while third term − second term is \((18-3c)-(18-c)=-2c\). Therefore, \(-c=-2c\), which gives \(c=0\). For \(c=1\) or \(c=3\), the two differences are not equal. Exam tip: For three terms to be in AP, equate their two consecutive differences.
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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