Geometric Progression
Gujarat Board · Class 11 · Statistics
Quick revision notes for Geometric Progression — Gujarat Board Class 11 Statistics. Key concepts, formulas, and definitions for last-minute revision.
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Meaning and Definition of Geometric Progression
- A sequence where the ratio of consecutive terms is constant (non-zero)
- Each term is obtained by multiplying the previous term by a fixed number called common ratio (r)
- Examples: 3, 6, 12, 24... (r = 2); 4, -12, 36, -108... (r = -3); 2, 1, 1/2, 1/4... (r = 1/2)
Formula for nth Term
- General term formula: T(n) = ar^(n-1) where a is first term and r is common ratio
- The sequence can be written as: a, ar, ar², ar³, ar⁴...
- For any G.P., if first term and common ratio are known, any term can be calculated
Geometric Series and Sum Formulas
- Geometric series is the sum of terms of a geometric progression
- Sum of first n terms is denoted by S(n)
- Different formulas for r = 1 and r ≠ 1 cases
Three Consecutive Terms in G.P.
- Special form for three consecutive terms: a/r, a, ar
- This form simplifies calculations when sum and product are given
- Middle term is 'a', other terms are obtained by dividing and multiplying by r
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