CBSE Mathematics 2026–27 · Topic 3

Sequences and Progressions

Understand the idea, practise the reasoning and apply it in an investigation. These original notes follow the regular Class IX Mathematics syllabus; the Advanced course is separate.

What to learn

Be able to explain the key result, choose a method that fits the question, show reasoning clearly and verify the answer.

Core concepts

A sequence is an ordered list. An explicit rule gives the nth term; a recursive rule builds a term from earlier term(s).
In an arithmetic progression (AP), the common difference d is fixed and aₙ=a+(n−1)d. The sum of the first n natural numbers is n(n+1)/2.
In a geometric progression (GP), each term is multiplied by a fixed ratio r and aₙ=arⁿ⁻¹. Repeated doubling appears in fractals and in the Tower of Hanoi, whose minimum moves are 2ⁿ−1.

Original CBSE-style solved examples

Attempt each calculation before reading the solution.

Example · AP term

For 7, 11, 15, …, a=7 and d=4. The 10th term is 7+9×4=43.

Example · GP and recursion

For 3, 6, 12, …, a=3 and r=2. The 8th term is 3×2⁷=384. A recursive rule is a₁=3 and aₙ=2aₙ₋₁.

Practice questions with answers

1. Find the 12th term of 5, 8, 11, …

a₁₂=5+11×3=38.

2. How many minimum moves are needed for 4 disks in the Tower of Hanoi?

2⁴−1=15.

Practical investigation

Fold a strip of paper repeatedly. Record the number of equal regions after each fold, then give a recursive and explicit rule.

Keep a record of materials, steps, observations and conclusion.

Self-check

Can I state the definition or theorem precisely?
Can I explain why the method applies?
Did I check signs, units, labels and the final result?

Use your prescribed NCERT textbook and teacher’s sequence. These are original study notes, not copied textbook answers.