If (2, 5, 10, 17) is called an arithmetic progression, what does the correct check show?
Answer and explanation
Correct answer: It is not an arithmetic progression because the differences are (3,5,7)
The defining condition of an arithmetic progression is that the difference between every pair of consecutive terms must be the same constant. Calculate the successive differences: 5-2=3, 10-5=5, and 17-10=7. Since 3, 5, and 7 are unequal, no single common difference exists, so the sequence is not an arithmetic progression. Option C states this exact reason and is correct. Merely increasing terms do not guarantee an AP; for example, their gaps may change, as they do here. Positive differences alone are also insufficient, so option B is false. The size of the first term has no bearing on the definition, making option D irrelevant.
Frequently asked questions
What is the correct answer to this question?
It is not an arithmetic progression because the differences are (3,5,7)
Why is this the correct answer?
The defining condition of an arithmetic progression is that the difference between every pair of consecutive terms must be the same constant. Calculate the successive differences: 5-2=3, 10-5=5, and 17-10=7. Since 3, 5, and 7 are unequal, no single common difference exists, so the sequence is not an arithmetic progression. Option C states this exact reason and is correct. Merely increasing terms do not guarantee an AP; for example, their gaps may change, as they do here. Positive differences alone are also insufficient, so option B is false. The size of the first term has no bearing on the definition, making option D irrelevant.
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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