+16 Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
+26367 Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
$$\small{\text{$
\begin{array}{rcl}
t_1 &=& -2\qquad r = \dfrac{8}{-2}=-4\\\\
t_n &=& t_1 \cdot r^{n-1}\\\\
t_n &=& (-2) \cdot (-4)^{n-1}\\\\
t_n &=& (-2) \cdot (-4)^n\cdot (-4)^{-1}\\\\
t_n &=& (-2)(-4)^{-1} \cdot (-4)^n\\\\
t_n &=& \frac{-2}{-4} \cdot (-4)^n\\\\
\mathbf{t_n} & \mathbf{=} & \mathbf{ \frac{1}{2} \cdot (-4)^n }
\end{array}
$}}$$
+26367 Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
$$\small{\text{$
\begin{array}{rcl}
t_1 &=& -2\qquad r = \dfrac{8}{-2}=-4\\\\
t_n &=& t_1 \cdot r^{n-1}\\\\
t_n &=& (-2) \cdot (-4)^{n-1}\\\\
t_n &=& (-2) \cdot (-4)^n\cdot (-4)^{-1}\\\\
t_n &=& (-2)(-4)^{-1} \cdot (-4)^n\\\\
t_n &=& \frac{-2}{-4} \cdot (-4)^n\\\\
\mathbf{t_n} & \mathbf{=} & \mathbf{ \frac{1}{2} \cdot (-4)^n }
\end{array}
$}}$$
+118608 I just wanted to muck around with this question and show how all the answers can be tied together :))
I would normally just have stopped on the first line :)
Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
a=-2 r=-4
$$\\t_n=-2*(-4)^{n-1}\\\\
or\\\\
t_n=-2*(-4)^{n}(-4)^{-1}\\\\
t_n=\frac{-2}{-4}*(-4)^{n}\\\\
t_n=\frac{1}{2}*(-4)^{n}\\\\
t_n=\frac{1}{2}*(-1)^n*(4)^{n}\\\\
t_n=\frac{1}{2}*(-1)^n*(2^2)^{n}\\\\
t_n=\frac{1}{2}*(-1)^n*2^{2n}\\\\
t_n=(-1)^n*2^{2n-1}\\\\$$
