[tex]GEOMETRIC \: \: PROGRESSIONS \\ \\ \\
Given \: G.P. \: - \\ \\ \frac{4}{3} \: , \: \frac{16}{3} \: , \: \frac{64}{3} \: , \: \frac{256}{3} \: , \: \frac{1024}{3} \\ \\ First \: term \: \: = \: \frac{4}{3} \\ \\ Common \: ratio \: = \: 4 \\ \\ \\ Sn \: = \: \frac{a(1 - {r}^{n} )}{1 - r} \\ \\ We \: have \: to \: find \: sum \: of \: 5 \: terms \: \\ Hence \: \: , \: \: n \: \: = \: \: 5 \\ \\ S5 = \frac{ \frac{4}{3}(1 - {4}^{5}) }{1 - 4} \\ \\ S5 \: \: = \: \: \frac{4}{3} \times \frac{ - 1023}{ - 3} \\ \\ S5 \: \: = \: \: \frac{1364}{3} \: \: \: \: \: \: \: \: Ans.[/tex]
