Given Data,
[tex]\begin{gathered} a_1=15 \\ r=\frac{1}{3} \end{gathered}[/tex]The sum of first 10 terms can be determined as,
[tex]\begin{gathered} S_{10}=\frac{a_1(1-r^{10})}{1-r} \\ =\frac{15(1-(\frac{1}{3})^{10})}{1-\frac{1}{3}} \\ =\frac{15(3^{10}-1)\times3}{2\times3^{10}} \\ =22.4996 \\ \approx22.50 \end{gathered}[/tex]Thus, the required sum is 22.50.
