diketahui deret geometri suku ke-5 dan suku ke-7 masing-masing adalah [tex] 4\frac{1}{2} \: dan \: 1\frac{1}{8} \: hitunglah \: jumlah \: 8 \: suku \: pertam

[tex]U_{5} = 4 \frac{1}{2} = \frac{9}{2} \\ \\ a.r^{4}= \frac{9}{2} \\ \\ a= \frac{9}{2 .r^{4} } \\ \\ \\ U_{7} =1 \frac{1}{8} = \frac{9}{8} \\ \\ a.r^{6} = \frac{9}{8} \\ \\ \frac{9}{2.r^{4} }.r^{6} = \frac{9}{8} \\ \\ r^{2} = \frac{1}{4} \\ \\ r= \frac{1}{2} \\ \\ a= \frac{9}{2.r^{4} } = \frac{9}{2. (\frac{1}{2}) ^{4}} = \frac{9}{ \frac{1}{8} } =72[/tex]

[tex]S_{8} = \frac{a(1-r^{n}) }{1-r} = \frac{72(1- (\frac{1}{2})^{8}) }{1- \frac{1}{2} } = \frac{72( \frac{255}{256}) }{ \frac{1}{2} } = \frac{2295}{16} = 143\frac{7}{16} [/tex]