What is the common difference in the sequence (4,8,12,16,\ldots)?

(4)

The common difference in an arithmetic progression is the change from one term to the next. It is calculated by subtracting an earlier term from the following term. If the sequence is truly arithmetic, this result stays the same for all consecutive pairs. This idea works equally well for increasing and decreasing sequences, and the difference may be positive, zero, or negative.

For the given sequence, subtract the first term from the second: \(8-4=4\). The other differences confirm it: \(12-8=4\) and \(16-12=4\). Hence the common difference is \(4\), making choice B correct. The number 8 is a term of the sequence, but it is not the common difference; this distinction is important. Values 2 and 12 also do not represent the change between consecutive terms.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..