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