State the fifth and seventh terms of the sequence \(-2, -3, -4\frac{1}{2}, ...\)
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: A
Explanation
\(-2, -3, -4\frac{1}{2}, ...\) This is a G.P with r = 1\(\frac{1}{2}\). \(T_{n} = ar^{n - 1}\) (terms of a G.P) \(T_{5} = (-2)(\frac{3}{2})^{5 - 1}\) = \(-2 \times \frac{81}{16}\) = \(-\frac{81}{8}\) \(T_{7} = (-2)(\frac{3}{2})^{7 - 1}\) = \(-2 \times \frac{729}{64}\) = \(-\frac{729}{32}\)
