Q1
What is a geometric progression?
AA sequence with a constant common ratio
BA sequence with a constant common difference
CA sequence with no pattern
DA sequence that always decreases
ICSEClass 10 (ICSE)MathematicsCh 11 · Topic 1
Geometric Progression
A geometric progression (GP) is a sequence where each term is found by multiplying the previous term by a constant, called the common ratio.
Core concept
The nth term of a GP is calculated as aₙ = a×r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
How it works
The sum of the first n terms of a GP is Sₙ = a(rⁿ-1)/(r-1) (for r≠1), useful for quickly finding totals.
Why it matters
A GP can be identified by checking if the ratio between consecutive terms remains constant throughout the sequence.
Key detail
Geometric progressions have real-life applications, like compound interest growth, population growth, and radioactive decay calculations.
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Quick notes
• GP: each term multiplied by a constant common ratio.
• nth term: aₙ = a×r^(n-1).
• Sum formula: Sₙ = a(rⁿ-1)/(r-1), r≠1.
• Common ratio must stay constant.
• This identifies a sequence as a GP.
• Real-life uses: compound interest, population growth.
• Radioactive decay also follows GP patterns.
• Practice builds GP problem-solving skills.