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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.

$-\frac{21}{8}, \frac{32}{618}$

View answer & explanation

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)

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

= $-2 \times \frac{81}{16}$

= $-\frac{81}{8}$

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

= $-2 \times \frac{729}{64}$

= $-\frac{729}{32}$

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