What is the common difference of (\frac{2}{3},\frac{5}{3},\frac{8}{3},\frac{11}{3},\ldots)?
Answer and explanation
Correct answer: (1)
Compute the difference between consecutive fractional terms: d=5/3−2/3=(5−2)/3=3/3=1. Checking the next pair gives 8/3−5/3=3/3=1, so the difference is constant and the sequence is an arithmetic progression. Thus option B is correct. The numerator increases by 3 while the denominator remains 3, producing an increase of one whole unit, not one-third.
Frequently asked questions
What is the correct answer to this question?
(1)
Why is this the correct answer?
Compute the difference between consecutive fractional terms: d=5/3−2/3=(5−2)/3=3/3=1. Checking the next pair gives 8/3−5/3=3/3=1, so the difference is constant and the sequence is an arithmetic progression. Thus option B is correct. The numerator increases by 3 while the denominator remains 3, producing an increase of one whole unit, not one-third.
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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