Geometric Progression — Chapter Summary
Gujarat Board · Class 11 · Statistics
Summary of Geometric Progression for Gujarat Board Class 11 Statistics. Part of the Gujarat Board Class 11 Statistics syllabus.
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Overview
A Geometric Progression (G.P.) is a special type of sequence where each term after the first is obtained by multiplying the previous term by a constant value called the common ratio. Unlike Arithmetic Progression where we add a constant difference, in G.P. we multiply by a constant ratio. This conce
Key Concepts
A sequence where the ratio
A sequence where the ratio of any term to its preceding term is constant (non-zero). This constant ratio is called the common ratio 'r'. For example:
The constant value by which each
The constant value by which each term is multiplied to get the next term. r = T(n+1)/Tn. It can be positive, negative, or fractional (but never zero).
Tn = ar^(n
Tn = ar^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the position of the term. This helps find any term without calculating
When r = 1
When r = 1: Sn = na. When r ≠ 1: Sn = a(r^n - 1)/(r - 1) or Sn = (rTn - a)/(r - 1). These formulas help calculate the total of first n terms.
When three consecutive terms are unknown
When three consecutive terms are unknown, they can be represented as a/r, a, ar. This simplifies calculations compared to using a, ar, ar².
Learning Objectives
- Understand the meaning and definition of Geometric Progression
- Learn the formula for finding the nth term of a G.P.
- Distinguish between Geometric Progression and Geometric Series
- Apply formulas to calculate sum of first n terms
- Solve problems involving three consecutive terms of G.P.
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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