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State the fifth and seventh terms of the sequence \(-2, -3, ...

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 is A

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

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

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

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

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

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

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

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

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