Sequences and Series Flashcards

Grade 10 · Math · Flashcards

All key formulas and definitions for arithmetic and geometric sequences and series.

Flashcards

Sequence: An ordered list of numbers, each called a term
Arithmetic sequence: Each term differs from the previous by a constant d (common difference)
Geometric sequence: Each term is multiplied by a constant r (common ratio)
Common difference d: d = aₙ - aₙ₋₁; found by subtracting any term from the next
Common ratio r: r = aₙ / aₙ₋₁; found by dividing any term by the previous
Arithmetic nth term: aₙ = a₁ + (n - 1)d
Geometric nth term: aₙ = a₁ · rⁿ⁻¹
Arithmetic series sum: Sₙ = n/2 · (a₁ + aₙ) or Sₙ = n/2 · (2a₁ + (n-1)d)
Finite geometric series sum: Sₙ = a₁ · (1 - rⁿ) / (1 - r), where r ≠ 1
Series: The sum of terms in a sequence
Explicit formula: A formula that gives any term directly using its position n; both arithmetic and geometric nth-term formulas are explicit
Recursive formula: Defines each term using the previous term(s), e.g., aₙ = aₙ₋₁ + d
Sum of first n positive integers: 1 + 2 + ... + n = n(n+1)/2 (a special arithmetic series)