Answer:
n = 8
Step-by-step explanation:
This is a geometric sequence where the sum to n terms is
[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]
where a is the first term and r the common ratio
r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 and a = 2, thus
[tex]\frac{2(3^n-1)}{3-1}[/tex] = 6560
[tex]\frac{2(3^n-1)}{2}[/tex] = 6560 ← cancel the 2
[tex]3^{n}[/tex] - 1 = 6560 (add 1 to both sides )
[tex]3^{n}[/tex] = 6561
note that 6561 = [tex]3^{8}[/tex], hence
[tex]3^{n}[/tex] = [tex]3^{8}[/tex] ⇒ n = 8
