If a geometric series is given by a n = 2 * (1/3)^x, find a 2 , find S, and find S 3

54 = 76

I suppose you mean a_n= 2 * (1/3)^n

a₂ 

\(=2\times(\dfrac{1}{3})^2\\ =\dfrac{2}{9}\) 

S_n OR S 

\(=\dfrac{a_1(1-r^n)}{1-r}\\ =\dfrac{2\times(\dfrac{1}{3})^1\times(1-\dfrac{1}{3^n})}{1-\dfrac{1}{3}}\\ =\dfrac{3^n-1}{3^n}\)

S₃

\(=\dfrac{3^3-1}{3^3}\\ =\dfrac{26}{27}\)