Odpowiedź:
[tex]a_{n} = 3 *2^{n-1}[/tex] , [tex]S_{10} =[/tex] 3069
Szczegółowe wyjaśnienie:
[tex]a_{1} = 3[/tex]
[tex]a_{6} = 96[/tex]
WZÓR: [tex]a_{n} = a_{1} *q^{n-1}[/tex]
[tex]a_{6} = a_{1} *q^{6-1}[/tex]
[tex]a_{6} = a_{1} *q^{5}[/tex]
96 = 3 * [tex]q^{5}[/tex] /:3
[tex]q^{5} = 32[/tex]
q = 2
Wzór ogólny tego ciągu : [tex]a_{n} = 3 *2^{n-1}[/tex]
[tex]S_{n} = a_{1} * \frac{1-q^{n} }{1-q}[/tex]
[tex]S_{10} = 3 * \frac{1-2^{10} }{1-2}[/tex] = 3 * [tex]\frac{1-1024}{-1}[/tex] = 3 * 1023 = 3069
