What is the common difference of 1/2, 1, 3/2, 2, …?
Answer and explanation
Correct answer: 1/2
The common difference of an arithmetic progression is found by subtracting any term from the term immediately after it. Using the first two terms, d = 1 − 1/2 = 1/2. Checking the next pairs confirms the result: 3/2 − 1 = 1/2 and 2 − 3/2 = 1/2. Thus the sequence increases by one-half at every step, so its common difference is 1/2. Option A is correct. The values 1, 3/2, and 2 are terms of the sequence, not the fixed amount added between consecutive terms. Working with fractions requires a common denominator, but here the subtraction is direct.
Frequently asked questions
What is the correct answer to this question?
1/2
Why is this the correct answer?
The common difference of an arithmetic progression is found by subtracting any term from the term immediately after it. Using the first two terms, d = 1 − 1/2 = 1/2. Checking the next pairs confirms the result: 3/2 − 1 = 1/2 and 2 − 3/2 = 1/2. Thus the sequence increases by one-half at every step, so its common difference is 1/2. Option A is correct. The values 1, 3/2, and 2 are terms of the sequence, not the fixed amount added between consecutive terms. Working with fractions requires a common denominator, but here the subtraction is direct.
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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