[tex]\displaystyle\bf\\b_{3} =24\\\\q=3\\\\S_{5} =?\\\\\\b_{3} =b_{1} \cdot q^{2} \\\\b_{1} =b_{3} :q^{2} =24:3^{2} =24:9=2\frac{2}{3} \\\\\\S_{5} =\frac{b_{1} \cdot(q^{5}-1) }{q-1} =\frac{2\frac{2}{3} \cdot(3^{5} -1)}{3-1} =\frac{2\frac{2}{3} \cdot(243 -1)}{2} =\\\\\\=\frac{2\frac{2}{3} \cdot 242}{2}=\frac{8}{3} \cdot 121=322\frac{2}{3} \\\\\\Otvet \ : \ S_{5} =322\frac{2}{3}[/tex]