Knowledge organisers

Arithmetic Progressions: CBSE Class 10 Maths knowledge organiser

Everything to know about arithmetic 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

Arithmetic progression (AP): A list of numbers where each term is the previous term plus a fixed number d.
Common difference: d = aₙ₊₁ − aₙ, the same all the way along an AP.
nth term: aₙ = a + (n − 1)d gives any term from its position.

Key formulas

\(n\)th term	\(a_n=a+(n-1)d\)
Sum of first \(n\) terms	\(S_n=\frac n2\big[2a+(n-1)d\big]=\frac n2(a+l)\)
From \(S_n\)	\(a_n=S_n-S_{n-1}\)
\(n\)th term from the end (last term \(l\))	\(l-(n-1)d\)
Three terms in AP; middle term	\(a-d,\ a,\ a+d;\) \(b=\frac{a+c}2\)
Natural numbers	\(1+2+\cdots+n=\frac{n(n+1)}2\)

Worked example

Which term of \(5, 9, 13, \ldots\) is \(101\)? \(5 + 4(n - 1) = 101 \Rightarrow n = 25\).

Common mistakes

Using \(a + nd\) instead of \(a + (n-1)d\).
Finding the number of terms as \(\dfrac{l - a}{d}\) and forgetting the “\(+1\)”.
Confusing \(a_n\) (one term) with \(S_n\) (a sum).
Rejecting a second valid value of \(n\) when both give the same sum (negative terms can cancel).

You should be able to…

Spot an AP, find its common difference and any term, and count how many terms a list has.
Use Sₙ confidently, find a term from the end and solve the standard board questions on sums of multiples.
Write complete 5-mark answers on AP word problems (savings, instalments, rows of seats) with a, d and n stated.
Handle Sₙ given as a formula, 'three numbers in AP' and sums of the next n terms, the 95+ questions.

The printable sheet

Arithmetic Progressions knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Arithmetic Progressions knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers