Answer:
[tex]S_{n}[/tex] = 11([tex]2^{n}[/tex] - 1)
Step-by-step explanation:
The sum to n terms of a geometric sequence is
[tex]S_{1n[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 11 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{22}{11}[/tex] = 2 , then
[tex]S_{n}[/tex] = [tex]\frac{11(2^{n}-1) }{2-1}[/tex] = 11 ([tex]2^{n}[/tex] - 1)
