Sequences and Series — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Sequences and Series, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Sequences and Series in one look
an ordered list of numbers, and what happens when you add it up
Sequence vs series
- a sequence is an ordered list a_1, a_2, a_3, ... , one number for every position n
- a series is what you get by adding the terms of a sequence together: a_1+a_2+a_3+…
- a_n, the nth term, is usually given by a formula in n, so any term can be found without listing every one before it
- a sequence can be finite (it stops) or infinite (it never does)
Arithmetic progression (AP): a fixed amount added each time
- nth term, first term a, common difference d
a_n=a+(n-1)d - common difference: any term minus the one before it
d=a_n-a_n-1 - sum of the first n terms
S_n=n/2left[2a+(n-1)dright] - sum, written with the last term l instead of d
S_n=n/2(a+l)
Arithmetic mean
- the arithmetic mean of two numbers a and b is A=a+b/2, the number exactly halfway between them
- a, A, b is then a 3-term AP: A-a=b-A, the same common difference on both sides
- inserting n arithmetic means between a and b makes an AP of n+2 terms total, a and b included
Geometric progression (GP): a fixed ratio multiplied each time
- nth term, first term a, common ratio r
a_n=a r^n-1 - common ratio: any term divided by the one before it
r=a_n/a_n-1 - sum of the first n terms, r≠1
S_n=a(r^n-1)/r-1 - sum to infinity, only when |r|<1
S_∞=a/1-r
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Sequences and Series sheet covers
- Sequence vs series
- Arithmetic progression (AP): a fixed amount added each time
- nth term, first term a, common difference d
- common difference: any term minus the one before it
- sum of the first n terms
- sum, written with the last term l instead of d
- Arithmetic mean
- How AP terms grow
- Geometric progression (GP): a fixed ratio multiplied each time
- nth term, first term a, common ratio r
- common ratio: any term divided by the one before it
- sum of the first n terms, r≠1
- sum to infinity, only when |r|<1
- How GP terms grow, r > 1
- Geometric mean
- AP or GP
- Sum of an AP
- Sum of special series
- Checking a sum-of-squares formula
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Sequences and Series the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.