
A.
(frac{x}{y}) 
B.
(frac{y}{x}) 
C.
((frac{x}{y}))^{(frac{1}{n – 2})} 
D.
((frac{y}{x}))^{(frac{1}{n – 2})}
Correct Answer: Option D
Explanation
Sum of nth term of a G.P = Sn = (frac{ar^n – 1}{r – 1})
sum of the first two terms = (frac{ar^2 – 1}{r – 1})
x = a(r + 1)
sum of the last two terms = S_{n} – S_{n – 2}
= (frac{ar^n – 1}{r – 1}) – (frac{(ar^{n – 1})}{r – 1})
= (frac{a(r^n – 1 – r^{n – 2} + 1)}{r – 1}) (r^{2} – 1)
∴ (frac{ar^{n – 2}(r + 1)(r – 1)}{1})= ar^{n} – 2(r + 1) = y
= a(r + 1)r^^{n – 2}
y = xr^{n – 2}
= yr^{n – 2}
(frac{y}{x}) = r = ((frac{y}{x}))^{(frac{1}{n – 2})}