What is the common difference of (x, x + √5, x + 2√5, x + 3√5)?
Answer and explanation
Correct answer: √5
The common difference is the amount added to obtain each next term. Subtracting the first term from the second gives (x + √5) − x = √5. The next subtraction gives (x + 2√5) − (x + √5) = √5, and the third gives (x + 3√5) − (x + 2√5) = √5. Thus the sequence is an arithmetic progression with common difference √5, so option B is correct. The variable x is the initial or fixed part and cancels when consecutive terms are subtracted. Option C doubles the actual step, while option D is a term, not the difference.
Frequently asked questions
What is the correct answer to this question?
√5
Why is this the correct answer?
The common difference is the amount added to obtain each next term. Subtracting the first term from the second gives (x + √5) − x = √5. The next subtraction gives (x + 2√5) − (x + √5) = √5, and the third gives (x + 3√5) − (x + 2√5) = √5. Thus the sequence is an arithmetic progression with common difference √5, so option B is correct. The variable x is the initial or fixed part and cancels when consecutive terms are subtracted. Option C doubles the actual step, while option D is a term, not the difference.
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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