CBSE Math RevisionSequences and Series: CBSE Class 11 Maths knowledge organiser
Everything to know about sequences and series 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.
Key definitions
- Geometric progression
- A sequence where each term is the previous one times a fixed ratio r.
- Arithmetic mean
- The AM of a and b is (a + b)/2.
- Geometric mean
- The GM of positive a and b is √(ab).
Key formulas
| GP | \(a_n=ar^{n-1},\) \(S_n=\frac{a(r^n-1)}{r-1}\ (r\ne1)\) |
| Infinite GP, \(|r|<1\) | \(S_\infty=\frac a{1-r}\) |
| AM, GM; \(A\ge G\) | \(A=\frac{a+b}2,\) \(G=\sqrt{ab}\) |
Worked example
Find the sum of the first \(7\) terms of \(2, 6, 18, \ldots\)
\(S_7 = \dfrac{2(3^7 - 1)}{3 - 1} = 3^7 - 1 = 2186\).
Common mistakes
- \(a_n = ar^n\) instead of \(ar^{n-1}\).
- Using \(S_\infty\) when \(|r| \ge 1\): the sum does not exist.
- Taking the ratio as \(\dfrac{a_1}{a_2}\) instead of \(\dfrac{a_2}{a_1}\), especially with negative ratios.
- Forgetting that the GM needs positive numbers.
You should be able to…
- Find terms, sums and sums to infinity of GPs and the AM and GM of two numbers.
- Find a GP from two of its terms, insert means and convert recurring decimals.
- Sum series built from GPs and model bouncing balls and savings plans.
- Use AM ≥ GM and combine conditions on S∞ and partial sums.
The printable sheet
Revise it next
- Sequences and Series: Class 11 notes
- Practise Sequences and Series by step (Route to 95)
- Skill Builders
- CBSE Class 11 Maths formula sheet (PDF)
Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers