[tex]t_n = a r^{n-1} [/tex]
a = 4, r = 3, [tex]t_n = 8748[/tex]
No rounding needed? It's a whole number
[tex]8748 = 4 \cdot 3^{n-1} \\
\\ \displaystyle\frac{8748}{4} = 3^{n-1} \\ \\
2187 = 3^{n-1} \\ \\
\log_3(2187) = n - 1 \implies n = \log_3(2187) + 1 \implies \\ \\ \\
n = \frac{\ln 2187}{\ln 3} + 1 = 7 + 1 = 8[/tex]
[tex]\displaystyle S_n=\frac{a(1-r^n)}{1-r} \implies S_8 =\displaystyle \frac{4(1 - 3^8)}{1 - 3} \\ \\ \\
= 13120[/tex]
Sum is 13120
