What is (d) in the arithmetic progression (\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots)?
Answer and explanation
Correct answer: (\frac{1}{3})
The common difference of an arithmetic progression is found by subtracting one term from the following term. For the given sequence, use the first two terms: \(d=\frac{2}{3}-\frac{1}{3}\). The denominators are already equal, so subtracting the numerators gives \(d=\frac{1}{3}\). Checking the next pair gives \(1-\frac{2}{3}=\frac{1}{3}\), and the following pair gives \(\frac{4}{3}-1=\frac{1}{3}\).
Thus the common difference is \(\frac{1}{3}\), so option A is correct. The value \(\frac{2}{3}\) is the second term, not the difference. Similarly, 1 and \(\frac{4}{3}\) are later terms. Equal differences confirm that the listed sequence is an arithmetic progression.
Frequently asked questions
What is the correct answer to this question?
(\frac{1}{3})
Why is this the correct answer?
The common difference of an arithmetic progression is found by subtracting one term from the following term. For the given sequence, use the first two terms: \(d=\frac{2}{3}-\frac{1}{3}\). The denominators are already equal, so subtracting the numerators gives \(d=\frac{1}{3}\). Checking the next pair gives \(1-\frac{2}{3}=\frac{1}{3}\), and the following pair gives \(\frac{4}{3}-1=\frac{1}{3}\).
Thus the common difference is \(\frac{1}{3}\), so option A is correct. The value \(\frac{2}{3}\) is the second term, not the difference. Similarly, 1 and \(\frac{4}{3}\) are later terms. Equal differences confirm that the listed sequence is an arithmetic progression.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
