[tex]a_1 = 4\\q = 5\\S_{n} = 3124\\n = ?[/tex]
Wzór na sumę n-tych wyrazów ciągu geometrycznego:
[tex]S_{n} = a_1\cdot\frac{1-q^{n}}{1-q}\\\\3124=4\cdot\frac{1-5^{n}}{1-5}\\\\3124=4\cdot\frac{1-5^{n}}{-4}\\\\3124=-(1-5^{n})\\\\1-5^{n} = -3124\\\\-5^{n} = -3124-1\\\\-5^{n} = -3125 \ \ /\cdot(-1)\\\\5^{n} = 3125\\\\5^{n} = 5^{5}\\\\\underline{n = 5}\\\\Odp. \ C. \ 5[/tex]
