What is the common difference of the arithmetic progression (3/4,5/4,7/4,9/4,\ldots)?
Answer and explanation
Correct answer: 1/2
The defining rule of an arithmetic progression is that consecutive terms differ by one fixed number. Since all the displayed fractions have the same denominator, subtract their numerators and retain the denominator. Thus, the difference between the first two terms is 5/4 − 3/4 = 2/4 = 1/2. The next differences agree: 7/4 − 5/4 = 2/4 = 1/2 and 9/4 − 7/4 = 1/2. Hence the common difference is 1/2, making option B correct. Option A results from subtracting the numerators incorrectly as one unit; option C is the first term; and option D is not the difference between consecutive terms.
Frequently asked questions
What is the correct answer to this question?
1/2
Why is this the correct answer?
The defining rule of an arithmetic progression is that consecutive terms differ by one fixed number. Since all the displayed fractions have the same denominator, subtract their numerators and retain the denominator. Thus, the difference between the first two terms is 5/4 − 3/4 = 2/4 = 1/2. The next differences agree: 7/4 − 5/4 = 2/4 = 1/2 and 9/4 − 7/4 = 1/2. Hence the common difference is 1/2, making option B correct. Option A results from subtracting the numerators incorrectly as one unit; option C is the first term; and option D is not the difference 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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