The first term of a geometric progression is 350. If the sum to infinity is 250, find the common ratio.
-
A.
(frac{-5}{7}) -
B.
(-frac{2}{5}) -
C.
(frac{2}{5}) -
D.
(frac{5}{7})
Correct Answer: Option B
Explanation
(S_{infty} = frac{a}{1 – r}) (Sum to infinity of a GP)
(250 = frac{350}{1 – r} implies 250(1 – r) = 350)
(350 = 250 – 250r implies 350 – 250 = -250r)
(250r = -100 implies r = frac{-100}{250} = -frac{2}{5})