Chapter at a glance
Sequences and their rules (explicit and recursive), triangular numbers, arithmetic and geometric progressions, and fractals that produce geometric progressions.
What this chapter covers
- 8.1 Introduction to Sequences
- 8.2 Explicit Rule for a Sequence
- 8.3 Recursive Rule for a Sequence
- 8.4 Arithmetic Progressions
- 8.5 Sum of the First n Natural Numbers
- 8.6 Geometric Progressions
Key points
- An explicit rule uses the position n; a recursive rule uses earlier terms.
- Triangular numbers 1, 3, 6, 10, …: tₙ = n(n + 1)/2, which is also the sum 1 + 2 + … + n.
- AP: a, a + d, a + 2d, …; tₙ = a + (n − 1)d.
- GP: a, ar, ar², …; tₙ = arⁿ⁻¹. Fractals like the Sierpiński triangle lead to GPs.
Read the NCERT chapter
Read this chapter in the official NCERT textbook Ganita Manjari (2026-27 edition) for free on ncert.nic.in.
Source: NCERT, Ganita Manjari, Grade 9 (2026-27). NCERT chapter PDF. Spotted a mistake? Email edura.class9.yt@gmail.com. Last updated 11 October 2026.