Sequence & Series|High School|NCERT : Become an Expert

Learn everything there is to know about Arithmetic Progression, Geometric Progression and some more special series.

Created byAbhishek Mishra, IITian, PhD in Neuroscience

Last updated 6/2018

English

What you'll learn

Complete understanding of Arithmetic Progression (A.P.) with solved examples
Complete understanding of Geometric Progression (G.P.) with solved examples
nth term, Sum of n terms of an A.P., G.P.
Sum of first n natural numbers
1^2 + 2^2 + 3^2 .... n^2
Sum of special series like sum of cubes of first n natural numbers
Relationship between Arithmetic Mean, Geometric Mean

Course content

1 section • 18 lectures • 3h 7m total length

Which is your favourite pattern in Nature1:49
Introduction to Arithmetic Progression8:51
Explore arithmetic progression concepts by examining the first term, common difference, and how a fixed increment builds sequences like salary growth, square counts, and finite or infinite progressions.
Introduction to AP with Solved Examples5:58
Explore arithmetic progression basics: identify the first term and common difference, determine the difference from adjacent terms, and verify a fixed, positive, negative, or zero difference governs AP sequences.
nth term of an A.P.7:19
Compute the nth term of an arithmetic progression using starting value a and common difference d, with the formula a_n = a + (n-1)d, illustrated by salary growth.
nth term of an A.P. Solved Examples12:29
nth term of an A.P. Advance Examples16:26
Sum of n terms of an A.P.16:23
Learn the pairing method to sum the first n terms of an arithmetic progression, derive S_n = n/2 (a1 + a_n), and relate to Gauss's quick insight.
Sequence & Series Intro13:25
Explore sequences and progressions, from arithmetic and geometric progressions to the Fibonacci sequence, and learn series, sigma notation, and the idea of sequences as functions from natural numbers.
Properties of Arithmetic Progression6:08
Sum of n terms of an A.P. Advance examples13:18
Insert n number of terms between two given number - A.P.11:13
nth term of Geometric Progression8:41
Explore geometric progression by showing how the first term multiplies by a fixed ratio to yield subsequent terms, and understand the common ratio and the nth term.
Sum of n terms of G.P.6:57
Sum of 7+77+777+7777 + .... n terms12:24
Transform the sum of 7, 77, 777, ... up to n terms into a geometric progression using a ten-based trick; derive and apply the formula to find the total quickly.
Geometric Mean9:13
Relationship between A.M. & G.M.13:00
Explore the relationship between A.M. and G.M. through geometric interpretations of right triangles and diameters, and derive the AM-GM inequality algebraically.
Sum of series 5 + 11 + 19 + 29 + 41 + .... n terms11:21
Miscellaneous Examples12:53
Apply step-by-step reasoning to AP and GP problems, prove expressions form a GP, and use common ratios, arithmetic means, and common roots in miscellaneous sequence examples.

Requirements

Very basic Mathematics knowledge of Addition, Subtraction, Multiplication, Division
We'll start everything from scratch, and build to expertise level.

Description

We will learn everything about Arithmetic Progression, Geometric Progression and some special series - from deriving formulas for nth term, finding sum of first n terms, sum of first n natural numbers, sum of squares & cubes of first n natural numbers. The course will demonstrate many solved examples, for interesting real life questions. This course is for absolute beginner, and by the end of the course with some practice, you will become an expert in any Sequence & Series question. The course is highly useful for any school student and students preparing for competitive examinations like SAT, GRE, IIT JEE Mains & Advance.

Arithmetic Progression
Geometric Progression
Sum of first n natural numbers
Sum of squares & cubes of first n natural numbers
Special Series

Who this course is for:

Anyone who wants to learn Mathematics
High School Students
Students for Grade X CBSE, ICSE, State Boards in India
IIT JEE Mains Students