lightbulb Key Concepts

< div id = "study-notes" style = "background: rgba(255,255,255,0.03); padding: 1.5rem; border-radius: 12px; border: 1px solid rgba(255,255,255,0.1); margin-bottom: 2rem; line-height: 1.6;" >

1. Arithmetic Progression (AP)

A sequence where the difference between consecutive terms is constant (d).

• n-th Term: aₙ = a + (n-1)d
• Sum of n terms: Sₙ = n/2 [2a + (n-1)d]

2. Geometric Progression (GP)

A sequence where the ratio between consecutive terms is constant (r).

• n-th Term: aₙ = arⁿ⁻¹
• Sum of n terms: Sₙ = a(rⁿ - 1) / (r - 1) for r ≠ 1

3. Arithmetic Mean & Geometric Mean

• A.M. between a and b: (a + b) / 2
• G.M. between a and b: √(ab)