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how many terms of the geometric sequence give a sum of 1022 if a5 = 32, q = 0.5? do the math

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Answer to a math question how many terms of the geometric sequence give a sum of 1022 if a5 = 32, q = 0.5? do the math

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Adonis
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Abychom našli počet členů geometrické posloupnosti, které dávají součet 1022, musíme použít vzorec pro součet geometrické řady: Sn = a * (1 - q^n) / (1 - q) Vzhledem k tomu, že a5 (pátý člen) je 32 a q (společný poměr) je 0,5, můžeme tyto hodnoty vložit do vzorce: 1022 = 32 * (1–0,5^n) / (1–0,5) Zjednodušení rovnice: 1022 = 32 * (1 - 0,5^n) / 0,5 Vynásobením obou stran rovnice 0,5 odstraníte jmenovatele: 1022 * 0,5 = 32 * (1 – 0,5^n) 511 = 32 - 16^n Přeuspořádání rovnice: 16^n = 32 - 511 16^n = -479 Protože 16 umocněné na žádnou mocninu nemůže být záporné, neexistuje žádná celočíselná hodnota n, která by vyhovovala této rovnici. Proto neexistují žádné členy geometrické posloupnosti, které dávají součet 1022 s danými hodnotami a5 = 32 a q = 0,5.

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