✦ Class 11 · Maths

Sequences and Series

You'll see how a simple pattern can predict a virus spread or a bouncing ball's height!

What this lesson covers

Step by step, in this order.

1A sequence is an ordered list of terms, like steps on a staircase.
2An Arithmetic Progression (AP) has a constant common difference d; e.g., saving Rs 100 each month.
3The nth term of an AP: aₙ = a + (n‑1)d.
4A Geometric Progression (GP) has a constant common ratio r; each term = previous × r. Example: population doubling each year.
5GP nth term: aₙ = a·rⁿ⁻¹. Find the 6th term of 3, 6, 12, 24, … (unit: count).
6Sum of first n GP terms: Sₙ = a(rⁿ‑1)/(r‑1). Example: a = 2, r = 3, n = 5 (unit: rupees).
7Infinite GP (|r|<1) sum: S∞ = a/(1‑r). Example: 1, ½, ¼, ⅛,… (unit: meters). This resolves Zeno's paradox.
8Arithmetic Mean (AM) of a,b is (a+b)/2; Geometric Mean (GM) is √(ab). AM ≥ GM always.
9TRY IT: Insert a geometric mean between 4 and 9. Compute √(4·9)=6 (unit: count).
10Recap: sequences, AP, GP, sums, infinite series, and AM‑GM.

How it looks

This board is from a different Maths lesson — yours will look like this. She writes and draws while she explains, and stops to check you followed.

A sequence is just an ordered list of numbers or objects, like days of the month.
It’s the fixed amount added each step in an arithmetic progression.
It’s the fixed factor you multiply by each step in a geometric progression.
An infinite GP adds forever but can have a finite total if the ratio’s absolute value is less than one.
AM is the ordinary average; GM multiplies the numbers then takes the square root. AM is never smaller than GM.
Think of compound interest (GP) or a rumor spreading (GP) to see these ideas in action.

Class 11 Maths

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