What is the common difference of (1.5,2.0,2.5,3.0,\ldots)?
Answer and explanation
Correct answer: (0.5)
The common difference of an arithmetic progression is the fixed amount added to obtain each term from the preceding term. It is found by subtracting one term from the next, such as \(a_2-a_1\). The terms may be whole numbers, fractions, or decimals; the method remains exactly the same. Every pair of consecutive terms should give the same difference.
For this sequence, subtract the first term from the second: \(2.0-1.5=0.5\). The next checks agree: \(2.5-2.0=0.5\) and \(3.0-2.5=0.5\). Thus the constant difference is \(0.5\), so choice B is correct. The value \(0.25\) would be too small, while \(1.0\) and \(1.5\) do not equal the change between consecutive terms.
Frequently asked questions
What is the correct answer to this question?
(0.5)
Why is this the correct answer?
The common difference of an arithmetic progression is the fixed amount added to obtain each term from the preceding term. It is found by subtracting one term from the next, such as \(a_2-a_1\). The terms may be whole numbers, fractions, or decimals; the method remains exactly the same. Every pair of consecutive terms should give the same difference.
For this sequence, subtract the first term from the second: \(2.0-1.5=0.5\). The next checks agree: \(2.5-2.0=0.5\) and \(3.0-2.5=0.5\). Thus the constant difference is \(0.5\), so choice B is correct. The value \(0.25\) would be too small, while \(1.0\) and \(1.5\) do not equal the change between consecutive terms.
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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