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
\(-\frac{21}{8}, \frac{32}{618}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(-2, -3, -4\frac{1}{2}, ...\)
This is a G.P with r = 1\(\frac{1}{2}\).
\(T_{n} = ar^{n - 1}\) (terms of a G.P)
\(T_{5} = (-2)(\frac{3}{2})^{5 - 1}\)
= \(-2 \times \frac{81}{16}\)
= \(-\frac{81}{8}\)
\(T_{7} = (-2)(\frac{3}{2})^{7 - 1}\)
= \(-2 \times \frac{729}{64}\)
= \(-\frac{729}{32}\)
Source: Myschool Past Questions Archive (Record #23212)