Geometric Sequence

Given a geometric sequence where the 5th term = 162, and the 8th term = -4374, determine the first three terms of the sequence.

I am unclear how to do this when I was not given the first term or the common ratio. Please help!!

$$\begin{array}{rclr} \small{ \text{geometric sequence: } a_n &=& a_1\cdot r^{n-1} }\\\\ \small{ \text{we have: } a_5 &=& a_1\cdot r^{5-1} = a_1 \cdot r^4 = & 162 }\\ \small{ \text{and we have: } a_8 &=& a_1\cdot r^{8-1} = a_1 \cdot r^7 = & -4374 } \end{array}\\\\ \small{\text{If we divide }} a_5 \small{\text{ and } a_8, \small{\text{we can calculate the ratio r }}$$

$$\small{\text{ $ \begin{array}{rclr} \dfrac{ a_8 } { a_5 } &=& \dfrac{a_1\cdot r^7}{a_1 \cdot r^4} = \dfrac{-4374 }{ 162} \\\\ \dfrac{a_1\cdot r^7}{a_1 \cdot r^4} &=& \dfrac{-4374 }{ 162} \\\\ \dfrac{r^7}{r^4} &=& \dfrac{-4374 }{ 162} \\\\ r^{7-4} &=& \dfrac{-4374 }{ 162} \\\\ r^{3} &=& \dfrac{-4374 }{ 162} \\\\ r^{3} &=& -27 \qquad | \qquad \sqrt[3]{}\\\\ \mathbf{r} &\mathbf{=}&\mathbf{ -3 } \end{array} $}}$$

$$\small{\text{Now we can calculate the first term }} a_1 \small{\text{ with } a_5 \small{\text{ or } a_8$$

$$\small{\text{ $ \begin{array}{rclr} a_5 = a_1 \cdot r^4 &=& 162 \\\\ a_1 \cdot (-3)^4 &=& 162 \\\\ a_1 \cdot 81 &=& 162 \qquad | \qquad :81\\\\ \mathbf{a_1} &\mathbf{=}& \mathbf{2} \\\\ \end{array} $}}$$

$$\\\small{\text{check:}}\\ \small{\text{ $ \begin{array}{rclr} a_8 &=& a_1 \cdot r^7 \\\\ a_8 &=& 2\cdot (-3)^7 \\\\ a_8 &=& 2\cdot( -2187 )\\\\ \mathbf{a_8} &\mathbf{=}& \mathbf{-4374} \qquad \text{ okay } \\\\ \end{array} $}}$$