Sequences and Series — Class 11 Maharashtra HSC Mathematics revision notes
A 5-page visual revision sheet for Sequences and Series, written for Class 11 Maharashtra HSC 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
AP adds the same amount, GP multiplies the same factor, and HP is just a GP in disguise
Sequence, series, progression
- a sequence t_1,t_2,t_3,…,t_n,… is numbers in a definite order, finite or infinite
- a series is what you get by adding the terms of a sequence: t_1+t_2+t_3+…
- a sequence following a specific rule is a progression: AP, GP, HP, AGP here
AP, GP, HP at a glance
| Progression | Rule | nth term | Sum of n terms |
|---|---|---|---|
| AP | constant difference d | a+(n-1)d | n/2[2a+(n-1)d] |
| GP | constant ratio r | ar^n-1 | a(r^n-1)/r-1, r≠1 |
| HP | reciprocals form an AP | no direct formula | flip to AP, solve, flip back |
Arithmetic Progression, a recap
- constant common difference d=t_n+1-t_n
t_n=a+(n-1)d - sum of n terms
S_n=n/2left[2a+(n-1)dright]
Geometric Progression
- constant common ratio r=t_n+1/t_n
t_n=ar^n-1
Page 1 of 5. The full sheet, all 5 pages, opens free in the app.
What this Sequences and Series sheet covers
- Sequence, series, progression
- AP, GP, HP at a glance
- Arithmetic Progression, a recap
- constant common difference d=t_n+1-t_n
- sum of n terms
- Geometric Progression
- constant common ratio r=t_n+1/t_n
- Confirming a GP and finding a term
- Sum of n terms of a GP
- for r≠1
- Compound interest as a GP
- Sum to infinity of a GP
- only exists for |r|<1
- Summing an infinite GP
- Harmonic Progression
- definition
- The nth term of an HP
- Arithmetic, Geometric, Harmonic means of x, y
- A.M.
- G.M., same sign x,y
- H.M.
- link between all three
- Boundary values, sequences and series
- Why the AM-GM-HM chain holds for positive x,y
- Recovering two numbers from their means
- Arithmetico-Geometric Progression (AGP)
- each term is an AP term times a GP term
- nth term
- sum to infinity, |r|<1
- Identifying and summing an AGP
- Sum of powers of the first n natural numbers
- sum of the numbers themselves
- sum of their squares
- sum of their cubes
- A sum by splitting into two known sums
- Evaluating a general sigma expression
- 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.