\(a_1=7 \\
a_8=114688 \\ \\
a_n=a_1 \times r^{n-1} \\
a_8=a_1 \times r^7 \\
114688=7 \times r^7 \\
\frac{114688}{7}=r^7 \\
16384=r^7 \\
r=\sqrt[7]{16384} \\
r=4 \\ \\
S_n=\frac{a_1(1-r^n)}{1-r} \\ \Downarrow \\
S_8=\frac{7(1-4^8)}{1-4}=\frac{7(1-65536)}{-3}=\frac{7 \times (-65535)}{-3}=7 \times 21845=152915\)
The answer is 152,915.
