Arithmetic and Geometric Progression
ICSE · Class 10 · Mathematics
Quick revision notes for Arithmetic and Geometric Progression — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- A sequence is an arrangement of numbers following a certain rule
- A progression is a sequence that follows a specific pattern or rule
- There are two main types: Arithmetic Progression (A.P.) and Geometric Progression (G.P.)
Arithmetic Progression (A.P.)
- In A.P., the difference between consecutive terms is constant
- This constant difference is called 'common difference' (d)
- General form: a, a+d, a+2d, a+3d, ...
Geometric Progression (G.P.)
- In G.P., the ratio between consecutive terms is constant
- This constant ratio is called 'common ratio' (r)
- General form: a, ar, ar², ar³, ...
Special Cases and Applications
- Sum of first n natural numbers: 1+2+3+...+n = n(n+1)/2
- When selecting terms in A.P. with given sum: use (a-d), a, (a+d) for 3 terms
- When selecting terms in G.P. with given product: use a/r, a, ar for 3 terms
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