Odpowiedź:
[tex]a_2=25\\a_3=15\\[/tex]
[tex]q=\frac{15}{25}=\frac{3}{5}[/tex]
[tex]a_2=a_1q\\25=a_1*\frac{3}{5}\\a_1=25*\frac{5}{3}\\a_1=\frac{125}{3}[/tex]
[tex]S_6=\frac{125}{3}*\frac{1-(\frac{3}{5})^{6}}{1-\frac{3}{5}}=\frac{125}{3}*\frac{1-\frac{729}{15625}}{\frac{2}{5}}=\frac{125}{3}*\frac{\frac{14896}{15625}}{\frac{2}{5}}=\frac{125}{3}*\frac{14896}{15625}*\frac{5}{2}=\frac{5}{3}*\frac{7448}{625}*\frac{5}{1}=\frac{1}{3}*\frac{7448}{25}*\frac{1}{1}=\frac{7448}{75}[/tex]
[tex]a_2 = 25\\a_3 = 15[/tex]
więc
q = 15 : 25 = 0,6 = [tex]\frac{3}{5}[/tex]
[tex]a_2 = a_1*q = a_1*0,6 = 25\\a_1 = 25 : 0,6 = 250 : 6 = 41 \frac{4}{6} = 41 \frac{2}{3}[/tex]
[tex]S_8 = a_1 *\frac{1 - q^8}{1 - q} = \frac{125}{3} *\frac{1 - (3/5)^8}{1 - 3/5} =[/tex] [tex]\frac{125}{3}* \frac{1 - 6 561/390 625}{2/5} =\frac{125}{3} *\frac{5}{2} *\frac{384 064}{390 625} =[/tex]
[tex]= \frac{384 064}{6*625} = \frac{192 032}{1875} = 102 \frac{782}{1875}[/tex]
=========================
[tex]S_6 = a_1*\frac{1 - q^6}{1 - q} = \frac{125}{3} *\frac{1 - (3/5)*6}{1 -3/5} =[/tex] [tex]\frac{125}{3} *\frac{1 - \frac{729}{15 625} }{\frac{2}{5} } = \frac{125}{3}*\frac{5}{2} *\frac{14 896}{15 625} =[/tex]
[tex]= \frac{14 896}{6*25} = \frac{7 448}{75} = 99 \frac{23}{75}[/tex]
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Odpowiedź:
[tex]a_2=25\\a_3=15\\[/tex]
[tex]q=\frac{15}{25}=\frac{3}{5}[/tex]
[tex]a_2=a_1q\\25=a_1*\frac{3}{5}\\a_1=25*\frac{5}{3}\\a_1=\frac{125}{3}[/tex]
[tex]S_6=\frac{125}{3}*\frac{1-(\frac{3}{5})^{6}}{1-\frac{3}{5}}=\frac{125}{3}*\frac{1-\frac{729}{15625}}{\frac{2}{5}}=\frac{125}{3}*\frac{\frac{14896}{15625}}{\frac{2}{5}}=\frac{125}{3}*\frac{14896}{15625}*\frac{5}{2}=\frac{5}{3}*\frac{7448}{625}*\frac{5}{1}=\frac{1}{3}*\frac{7448}{25}*\frac{1}{1}=\frac{7448}{75}[/tex]
Odpowiedź:
[tex]a_2 = 25\\a_3 = 15[/tex]
więc
q = 15 : 25 = 0,6 = [tex]\frac{3}{5}[/tex]
[tex]a_2 = a_1*q = a_1*0,6 = 25\\a_1 = 25 : 0,6 = 250 : 6 = 41 \frac{4}{6} = 41 \frac{2}{3}[/tex]
[tex]S_8 = a_1 *\frac{1 - q^8}{1 - q} = \frac{125}{3} *\frac{1 - (3/5)^8}{1 - 3/5} =[/tex] [tex]\frac{125}{3}* \frac{1 - 6 561/390 625}{2/5} =\frac{125}{3} *\frac{5}{2} *\frac{384 064}{390 625} =[/tex]
[tex]= \frac{384 064}{6*625} = \frac{192 032}{1875} = 102 \frac{782}{1875}[/tex]
=========================
[tex]S_6 = a_1*\frac{1 - q^6}{1 - q} = \frac{125}{3} *\frac{1 - (3/5)*6}{1 -3/5} =[/tex] [tex]\frac{125}{3} *\frac{1 - \frac{729}{15 625} }{\frac{2}{5} } = \frac{125}{3}*\frac{5}{2} *\frac{14 896}{15 625} =[/tex]
[tex]= \frac{14 896}{6*25} = \frac{7 448}{75} = 99 \frac{23}{75}[/tex]
==========================
Szczegółowe wyjaśnienie: