--- title: "Progressione geometrica: definizione, proprietà, formule" description: Che cos’è una progressione geometrica? Questa videolezione spiega l'argomento passo dopo passo con esempi. url: https://astra-ai.co/it/videos/successioni/successione-geometrica/che-cos-e-una-progressione-geometrica/ locale: it type: video-lesson keywords: - che cos’è una progressione geometrica? - ragione - termine - successione published: 2026-10-01T10:12:08.064Z updated: 2026-10-04T23:21:02.560Z alternates: bg: https://astra-ai.co/bg/videos/posledovatelnosti/geometrichna-posledovatelnost/kakvo-e-geometrichna-posledovatelnost/ br: https://astra-ai.co/br/videos/sequencias/capitulo-matematica-033/video-matematica-064/ cs: https://astra-ai.co/cs/videos/sekvence/geometricke-sekvence/co-je-geometricka-posloupnost/ da: https://astra-ai.co/da/videos/foelger/geometrisk-foelge/hvad-er-en-geometrisk-f-lge/ de: https://astra-ai.co/de/videos/folgen/geometrische-folge/was-ist-eine-geometrische-folge/ el: https://astra-ai.co/el/videos/akolouthies/geometriki-akolouthia/what-is-a-geometric-sequence/ en: https://astra-ai.co/videos/sequences/geometric-sequence/what-is-a-geometric-sequence/ en-IN: https://astra-ai.co/en-IN/videos/sequences/chapter-5f43386f/what-is-a-geometric-sequence/ en-PH: https://astra-ai.co/en-PH/videos/sequences/chapter-5f43386f/lesson-fa8b3860/ es: https://astra-ai.co/es/videos/sucesiones/sucesion-geometrica/que-es-una-sucesion-geometrica/ es-AR: https://astra-ai.co/es-AR/videos/sucesiones/capitulo-27/que-es-una-sucesion-geometrica/ es-CL: https://astra-ai.co/es-CL/videos/sucesiones/capitulo-27/leccion-de-matematicas-64/ es-PE: https://astra-ai.co/es-PE/videos/sucesiones/capitulo-video-5f43386f/leccion-de-video-fa8b3860/ et: https://astra-ai.co/et/videos/jadad/geomeetriline-jada/mis-on-geomeetriline-jada/ fi: https://astra-ai.co/fi/videos/jonot/geometrinen-jono/mika-on-geometrinen-lukujono/ fr: https://astra-ai.co/fr/videos/suites/suite-geometrique/qu-est-ce-qu-une-suite-geometrique/ hr: https://astra-ai.co/hr/videos/nizovi/geometrijski-niz/sto-je-geometrijski-niz/ hu: https://astra-ai.co/hu/videos/sorozatok/mertani-sorozat/mi-az-a-mertani-sorozat/ id: https://astra-ai.co/id/videos/barisan/barisan-geometri/apa-itu-barisan-geometri/ it: https://astra-ai.co/it/videos/successioni/successione-geometrica/che-cos-e-una-progressione-geometrica/ ja: https://astra-ai.co/ja/videos/sequences-ja/27/064/ km: https://astra-ai.co/km/videos/sequences/chapter-5f43386f/lesson-fa8b3860/ ko: https://astra-ai.co/ko/videos/sequences-ko/27/064/ lo: https://astra-ai.co/lo/videos/lo-af25d53a/lo-5f43386f/lo-fa8b3860/ lt: https://astra-ai.co/lt/videos/sekos/geometrine-seka/pamoka-fa8b3860/ lv: https://astra-ai.co/lv/videos/virknes/geometriska-virkne/stunda-fa8b3860/ ms: https://astra-ai.co/ms/videos/jujukan/bab-33-matematik-asas/pelajaran-064/ ms-BN: https://astra-ai.co/ms-BN/videos/jujukan/bab-5f43386f/pelajaran-fa8b3860/ mx: https://astra-ai.co/mx/videos/sucesiones/capitulo-27/leccion-64/ my: https://astra-ai.co/my/videos/my-af25d53a/my-5f43386f/my-fa8b3860/ nl: https://astra-ai.co/nl/videos/reeksen/geometrische-reeks/wat-is-een-meetkundige-rij/ no: https://astra-ai.co/no/videos/folger/geometrisk-f-lge/hva-er-en-geometrisk-tallf-lge/ pl: https://astra-ai.co/pl/videos/ciagi/ciag-geometryczny/co-to-jest-ciag-geometryczny/ pt: https://astra-ai.co/pt/videos/sequencias/sequencia-geometrica/o-que-e-uma-sequencia-geometrica/ pt-TL: https://astra-ai.co/pt-TL/videos/sucessoes/capitulo-de-video-027/licao-de-video-064/ ro: https://astra-ai.co/ro/videos/siruri/progresie-geometrica/ce-este-o-progresie-geometrica/ sk: https://astra-ai.co/sk/videos/postupnosti/kapitola-027/lekcia-064/ sl: https://astra-ai.co/sl/videos/zaporedja/geometrijsko-zaporedje/kaj-je-geometrijsko-zaporedje/ sr: https://astra-ai.co/sr/videos/nizovi/poglavlje-027/lekcija-064/ sv: https://astra-ai.co/sv/videos/foljder/geometrisk-talfoljd/vad-ar-en-geometrisk-talfoljd/ th: https://astra-ai.co/th/videos/lamdap/bot-33-lam-dap-rekhakhanit/botrian-064/ tr: https://astra-ai.co/tr/videos/diziler/bolum-027/ders-064/ uk: https://astra-ai.co/uk/videos/uk-topic-14/uk-chapter-33/uk-lesson-fa8b3860/ vi: https://astra-ai.co/vi/videos/vi-topic-14/vi-chapter-33/cap-so-nhan-la-gi/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-014/shuxue-zhang-033/shuxue-kecheng-064/ zh-TW: https://astra-ai.co/zh-TW/videos/sequences/chapter-5f43386f/lesson-fa8b3860/ --- # Che cos’è una progressione geometrica? > Che cos’è una progressione geometrica? Questa lezione spiega il concetto e mostra i primi esempi. ## Definizione e caratteristiche Una progressione geometrica è definita da un primo termine `a1` e da un rapporto costante `r`: ogni termine è il precedente moltiplicato per `r`: `an = a1 * r^(n-1)` per `n >= 1`. Il rapporto `r` determina il comportamento: se `r > 1` la progressione cresce; se `0 < r < 1` decresce; se `r < 0` i termini alternano segno. Con `r = 1` è costante (`an = a1`). Nelle applicazioni, `r` modella tassi di crescita/decadimento (es. finanza). ## Formule e calcoli - n‑esimo termine: `an = a1 * r^(n-1)` - Somma dei primi n termini (per `r != 1`): `Sn = a1 * (1 - r^n) / (1 - r)`