Mathematics

State the fifth and seventh terms of the sequence (-2, -3, -4frac{1}{2}, …)

State the fifth and seventh terms of the sequence (-2, -3, -4frac{1}{2}, …)

  • A.
    (-frac{81}{8}, -frac{729}{32})
  • B.
    (frac{8}{81}, frac{72}{39})
  • C.
    (frac{27}{729}, frac{718}{39})
  • D.
    (-frac{27}{16}, -frac{79}{81})
  • E.
    (-frac{21}{8}, frac{32}{618})
Correct Answer: Option A
Explanation

(-2, -3, -4frac{1}{2}, …)

This is a G.P with r = 1(frac{1}{2}).

(T_{n} = ar^{n – 1}) (terms of a G.P)

(T_{5} = (-2)(frac{3}{2})^{5 – 1})

= (-2 times frac{81}{16})

= (-frac{81}{8})

(T_{7} = (-2)(frac{3}{2})^{7 – 1})

= (-2 times frac{729}{64})

= (-frac{729}{32})