What is the main identity of an arithmetic progression?

The difference of consecutive terms is equal

The defining property of an arithmetic progression is that the difference between every pair of consecutive terms is constant. If the terms are \(a_1,a_2,a_3,\ldots\), then \(a_2-a_1=a_3-a_2=a_4-a_3=d\), where \(d\) is the common difference. The terms can increase, decrease, or remain constant, so they need not all be positive.

For example, in \(3,7,11,15,\ldots\), each difference is 4, so it is an arithmetic progression. Equal ratios describe a geometric progression instead, not an arithmetic one. Likewise, squaring the previous term is not the defining rule, and negative or zero terms are allowed. Therefore the statement that consecutive terms have equal differences is correct, so choice B is the appropriate answer.

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