Is the sequence (4,8,13,19,\ldots) an arithmetic progression or not?
Answer and explanation
Correct answer: No, because the differences between consecutive terms are not equal
The differences between consecutive terms are 8−4=4, 13−8=5, and 19−13=6. In an arithmetic progression, the difference between every pair of consecutive terms must be constant. Since these differences are 4, 5, and 6, the sequence is not an arithmetic progression. Merely having increasing or positive terms is not sufficient. Exam tip: calculate consecutive differences to test whether a sequence is an AP.
Frequently asked questions
What is the correct answer to this question?
No, because the differences between consecutive terms are not equal
Why is this the correct answer?
The differences between consecutive terms are 8−4=4, 13−8=5, and 19−13=6. In an arithmetic progression, the difference between every pair of consecutive terms must be constant. Since these differences are 4, 5, and 6, the sequence is not an arithmetic progression. Merely having increasing or positive terms is not sufficient. Exam tip: calculate consecutive differences to test whether a sequence is an AP.
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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