Knowledge organisers

Sequences and Progressions: CBSE Class 9 Maths knowledge organiser

Everything to know about sequences and progressions on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Sequence: A list of numbers in a definite order: a₁, a₂, a₃, …
Arithmetic progression: A sequence that adds the same number d, the common difference, each time.
Recursive rule: Gives the first term and how each term comes from the one before.

Key formulas

AP; GP	\(a_n=a+(n-1)d;\) \(a_n=ar^{n-1}\)
Sum of naturals; of odd numbers	\(1+2+\cdots+n=\frac{n(n+1)}2;\) \(1+3+\cdots+(2n-1)=n^2\)
Fibonacci; Tower of Hanoi	\(F_{n+1}=F_n+F_{n-1};\) \(M_n=2M_{n-1}+1=2^n-1\)

Worked example

Which term of the AP \(4, 11, 18, \ldots\) is \(144\)?

\(4 + 7(n - 1) = 144 \Rightarrow n - 1 = 20 \Rightarrow n = 21\).

Common mistakes

\(a_n = a + nd\) instead of \(a + (n - 1)d\); similarly \(ar^n\) instead of \(ar^{n-1}\).
Calling a sequence an AP from its first two terms only: check that every difference is the same.
Ratio taken as \(\dfrac{a_1}{a_2}\) instead of \(\dfrac{a_2}{a_1}\).
Accepting a non-integer \(n\) when asked "which term": then the number is not a term.

You should be able to…

Continue a pattern, spot an AP or a GP and find a term from an explicit or recursive rule.
Find which term has a given value, find a and d from two terms and add 1 + 2 + … + n.
Model salaries, seating and growth with APs and GPs and answer every part of a case study.
Reason about fractals, the Tower of Hanoi and sums with exclusions such as 'not multiples of 5'.

The printable sheet

Sequences and Progressions knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Sequences and Progressions knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers