Arithmetic progression
- CBSE · NCERT Class 10, Ch 5 Arithmetic Progressions
An arithmetic progression, or AP, is a list of numbers in which the step from each number to the next never changes, as in 3, 7, 11, 15.
The fixed number is the common difference, written d. It can be positive, negative or zero. The first term is written a. Knowing a and d is enough to write the whole AP: a, a + d, a + 2d, a + 3d, and so on.
To test whether a list is an AP, subtract each term from the next. If every difference is the same, it is an AP. The rule that each term is the one before plus d is a recurrence relation.
A small example
- 3, 7, 11, 15, ... is an AP with a = 3 and d = 4.
- 10, 7, 4, 1, ... is an AP with a = 10 and d = -3.
- 1, 4, 9, 16, ... is not an AP. The differences are 3, 5 and 7, which change.
Where marks go
Board questions can hide an AP inside a story. Question 37 of CBSE's 2026-27 Maths Basic sample paper is one of its case-based questions, about planting trees. Each section plants three more trees than double its class number, and each class has two sections. So the classes plant 10, 14, 18, ... trees, an AP with d = 4.
In the board's Maths Basic marking scheme for 2026-27, part (i) is worth 1 mark and asks only for the common difference. Parts (ii) and (iii) then use the same AP for the other 3 marks. So spotting the AP and its d comes before every later mark in the question.
Sources
Facts last checked against these sources on 30 September 2026.
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