If (21,18,q,12,\ldots) is an arithmetic progression, what is the value of (q)?
Answer and explanation
Correct answer: \(15\)
In an arithmetic progression, the difference between consecutive terms is constant. Here, the common difference is \(d=18-21=-3\). Therefore, the third term is \(q=18+(-3)=15\). Checking: \(15-3=12\), so \(21,18,15,12\) is correct. If \(14\) were used, the consecutive differences would not be equal. Exam tip: Find \(d\) from the first two terms and apply the same difference to obtain the next term.
Frequently asked questions
What is the correct answer to this question?
\(15\)
Why is this the correct answer?
In an arithmetic progression, the difference between consecutive terms is constant. Here, the common difference is \(d=18-21=-3\). Therefore, the third term is \(q=18+(-3)=15\). Checking: \(15-3=12\), so \(21,18,15,12\) is correct. If \(14\) were used, the consecutive differences would not be equal. Exam tip: Find \(d\) from the first two terms and apply the same difference to obtain the next term.
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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