What is the common difference of (2p − q, 2p + 2q, 2p + 5q, 2p + 8q, …)?
Answer and explanation
Correct answer: 3q
Find the difference between consecutive terms rather than looking at the constant part of each expression. The first difference is (2p + 2q) − (2p − q) = 3q. The next difference is (2p + 5q) − (2p + 2q) = 3q, and the following one is (2p + 8q) − (2p + 5q) = 3q. Since the difference is constant, the sequence is an AP with d = 3q. Thus option D is correct. The 2p terms cancel during subtraction, so 2p is not the common difference. q and 2q also do not equal the actual change between consecutive terms.
Frequently asked questions
What is the correct answer to this question?
3q
Why is this the correct answer?
Find the difference between consecutive terms rather than looking at the constant part of each expression. The first difference is (2p + 2q) − (2p − q) = 3q. The next difference is (2p + 5q) − (2p + 2q) = 3q, and the following one is (2p + 8q) − (2p + 5q) = 3q. Since the difference is constant, the sequence is an AP with d = 3q. Thus option D is correct. The 2p terms cancel during subtraction, so 2p is not the common difference. q and 2q also do not equal the actual 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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