Home » Further Mathematics » The first term of a geometric progression is 350. If the sum to infinity is…

The first term of a geometric progression is 350. If the sum to infinity is…

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})