What is the common difference of the sequence (3a, 3a + 2b, 3a + 4b, 3a + 6b, …)?
Answer and explanation
Correct answer: 2b
The governing concept is that an arithmetic progression has a constant common difference, found by subtracting one term from the next. Here, (3a + 2b) − 3a = 2b. Also, (3a + 4b) − (3a + 2b) = 2b, and (3a + 6b) − (3a + 4b) = 2b. Since the same quantity is added at every step, the sequence is an AP with common difference 2b. Therefore, option C is correct. The terms 3a and a are not the difference: 3a is the fixed algebraic part, while a and b alone do not represent the change between consecutive terms.
Frequently asked questions
What is the correct answer to this question?
2b
Why is this the correct answer?
The governing concept is that an arithmetic progression has a constant common difference, found by subtracting one term from the next. Here, (3a + 2b) − 3a = 2b. Also, (3a + 4b) − (3a + 2b) = 2b, and (3a + 6b) − (3a + 4b) = 2b. Since the same quantity is added at every step, the sequence is an AP with common difference 2b. Therefore, option C is correct. The terms 3a and a are not the difference: 3a is the fixed algebraic part, while a and b alone do not represent the change 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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