Chapter-5 (Sequence and Series) Formulas

Sequence and Series: Important Formulas

Mathematics • Grade 10 • Sequence and Series

Quick memory: AP adds the same number (d); GP multiplies by the same number (r).

1. Arithmetic Sequence and Series

• Common differenced = t₂ − t₁
• General termtₙ = a + (n − 1)d
• Arithmetic mean of a and bm = (a + b)/2
• Total terms with m meansn = m + 2
• SumSₙ = n/2 [2a + (n − 1)d] or Sₙ = n/2 (a + l)

Special sums	Formula
First n natural numbers	n(n + 1)/2
First n odd numbers	n²
First n even numbers	n(n + 1)

2. Geometric Sequence and Series

• Common ratior = t₂ ÷ t₁
• General termtₙ = arⁿ⁻¹
• Geometric mean of a and bm = √(ab)
• Sum, r > 1Sₙ = a(rⁿ − 1)/(r − 1)
• Sum, r < 1Sₙ = a(1 − rⁿ)/(1 − r)
• Sum with last termSₙ = (lr − a)/(r − 1)

Exam tips: (1) For means, find d or r first by taking the last term as tₙ with n = m + 2. (2) Given t_p and t_q, divide (GP) or subtract (AP) the equations. (3) Quadratic in n may give two answers; check each.

Sequence and Series • Grade 10 Mathematics