Question

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 \(-\frac{21}{8}, \frac{32}{618}\)

Answer 1

The correct answer is A. \(-\frac{81}{8}, -\frac{729}{32}\)

\(-2, -3, -4\frac{1}{2}, ...\)

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

\(T_{n} = ar^{n - 1}\) (terms of a G.P)

\(T_{5} = (-2)(\frac{3}{2})^{5 - 1}\)

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

= \(-\frac{81}{8}\)

\(T_{7} = (-2)(\frac{3}{2})^{7 - 1}\)

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

= \(-\frac{729}{32}\)