A student says that the sequence \(7, 11, 15, 20, \ldots\) is an arithmetic progression because its terms are increasing. What is the error in the student's statement?
Answer and explanation
Correct answer: The differences between consecutive terms are not equal: \(11-7=4\), \(15-11=4\), but \(20-15=5\).
In an AP, the difference between every pair of consecutive terms must be constant. Here the differences are \(4,4,5\), so it is not an AP. Exam tip: check differences, not merely whether terms increase.
Frequently asked questions
What is the correct answer to this question?
The differences between consecutive terms are not equal: \(11-7=4\), \(15-11=4\), but \(20-15=5\).
Why is this the correct answer?
In an AP, the difference between every pair of consecutive terms must be constant. Here the differences are \(4,4,5\), so it is not an AP. Exam tip: check differences, not merely whether terms increase.
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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