{
  "unit": 9,
  "title": "Sequences, Series & the Binomial Theorem",
  "terms": [
    {
      "en": "arithmetic sequence",
      "es": "sucesión aritmética",
      "fr": "suite arithmétique",
      "ar": "متتالية حسابية",
      "pt": "sequência aritmética",
      "definition": "A sequence with a constant difference between consecutive terms."
    },
    {
      "en": "common difference",
      "es": "diferencia común",
      "fr": "raison arithmétique",
      "ar": "الفرق المشترك",
      "pt": "diferença comum",
      "definition": "The fixed value added to obtain each successive arithmetic term."
    },
    {
      "en": "explicit formula",
      "es": "fórmula explícita",
      "fr": "formule explicite",
      "ar": "صيغة صريحة",
      "pt": "fórmula explícita",
      "definition": "A rule computing the nth term directly from its index."
    },
    {
      "en": "geometric sequence",
      "es": "sucesión geométrica",
      "fr": "suite géométrique",
      "ar": "متتالية هندسية",
      "pt": "sequência geométrica",
      "definition": "A sequence with a constant nonzero ratio between consecutive terms where defined."
    },
    {
      "en": "common ratio",
      "es": "razón común",
      "fr": "raison géométrique",
      "ar": "النسبة المشتركة",
      "pt": "razão comum",
      "definition": "The multiplier connecting successive geometric terms."
    },
    {
      "en": "recursive formula",
      "es": "fórmula recursiva",
      "fr": "formule de récurrence",
      "ar": "صيغة عودية",
      "pt": "fórmula recursiva",
      "definition": "A rule computing a term from one or more preceding terms."
    },
    {
      "en": "sequence pattern",
      "es": "patrón de sucesión",
      "fr": "motif de suite",
      "ar": "نمط المتتالية",
      "pt": "padrão de sequência",
      "definition": "A consistent relationship among indexed terms."
    },
    {
      "en": "finite sequence",
      "es": "sucesión finita",
      "fr": "suite finie",
      "ar": "متتالية منتهية",
      "pt": "sequência finita",
      "definition": "A sequence having a specified finite number of terms."
    },
    {
      "en": "infinite sequence",
      "es": "sucesión infinita",
      "fr": "suite infinie",
      "ar": "متتالية غير منتهية",
      "pt": "sequência infinita",
      "definition": "A sequence with terms indexed indefinitely."
    },
    {
      "en": "series",
      "es": "serie",
      "fr": "série",
      "ar": "متسلسلة",
      "pt": "série",
      "definition": "The sum of terms from a sequence."
    },
    {
      "en": "sigma notation",
      "es": "notación sigma",
      "fr": "notation sigma",
      "ar": "ترميز سيغما للمجموع",
      "pt": "notação sigma",
      "definition": "A compact notation expressing indexed sums using the symbol Σ."
    },
    {
      "en": "sequence index",
      "es": "índice de sucesión",
      "fr": "indice de suite",
      "ar": "فهرس المتتالية",
      "pt": "índice de sequência",
      "definition": "The integer marking the position of a term."
    },
    {
      "en": "summation",
      "es": "sumatoria",
      "fr": "sommation",
      "ar": "المجموع المتسلسل",
      "pt": "somatório",
      "definition": "The operation of adding specified indexed terms."
    },
    {
      "en": "Pascal triangle",
      "es": "triángulo de Pascal",
      "fr": "triangle de Pascal",
      "ar": "مثلث باسكال",
      "pt": "triângulo de Pascal",
      "definition": "The array of binomial coefficients formed by adding adjacent numbers above."
    },
    {
      "en": "binomial coefficient",
      "es": "coeficiente binomial",
      "fr": "coefficient binomial",
      "ar": "معامل ثنائي الحدين",
      "pt": "coeficiente binomial",
      "definition": "The count n choose k of ways to select k objects from n."
    },
    {
      "en": "binomial theorem",
      "es": "teorema del binomio",
      "fr": "théorème du binôme",
      "ar": "نظرية ذات الحدين",
      "pt": "teorema binomial",
      "definition": "The formula expanding (a+b)^n using binomial coefficients for nonnegative integer n."
    }
  ],
  "schema_version": "1.1"
}