Arithmetic Progressions

An arithmetic progression is a list of numbers where the difference between consecutive terms stays constant. Such patterns appear in seating rows, savings plans and repeated schedules.

The first term is denoted by a and the common difference by d. Recognising whether a sequence is an AP is the first and most important step in this chapter.

The nth term helps us jump to any position in the progression without listing all terms. It is especially useful in board problems involving large term numbers.

The sum formula compresses long repeated addition into a neat algebraic rule. Students should know both the general sum formula and the version using first and last term.

By the end of the chapter, learners should be comfortable identifying APs, finding missing values, locating particular terms and summing terms quickly.