Sequences and Series
Uttar Pradesh Board · Class 11 · Mathematics
Quick revision notes for Sequences and Series — Uttar Pradesh Board Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction to Sequences
- A sequence is an ordered collection of numbers following a specific pattern
- Terms are denoted as a₁, a₂, a₃, ..., aₙ where subscripts indicate position
- The nth term (aₙ) is called the general term of the sequence
Series
- A series is the sum of terms of a sequence: a₁ + a₂ + a₃ + ... + aₙ
- Series can be finite (limited terms) or infinite (unlimited terms)
- Sigma notation (Σ) is used to represent series in compact form
Geometric Progression (G.P.)
- In G.P., each term (except first) bears constant ratio to preceding term
- Common ratio r = aₙ₊₁/aₙ (constant for all n)
- General form: a, ar, ar², ar³, ..., arⁿ⁻¹
Geometric Mean (G.M.)
- Geometric mean of two positive numbers a and b is √(ab)
- G.M. creates a G.P. when inserted between two numbers
- Multiple geometric means can be inserted between two numbers
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