The sum of the first two terms of a geometric progression is x and sum…

The sum of the first two terms of a geometric progression is x and sum of the last terms is y. If there are n terms in all, then the common ratio is

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}) (r² – 1)
∴ (frac{ar^{n – 2}(r + 1)(r – 1)}{1})= arⁿ – 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})}