Finding the first three terms of a geometric sequence, without the first term or common ratio. Given a geometric sequence where the $5$th term $= 162$ and the $8$th term $= -4374$, determine the first three terms of the sequence. 


I am unclear how to do this without being given the first term or the common ratio. please help!!
We have that $162 = a_{1}r^{4}$ and $-4374 = a_{1}r^{7}$ by the formula $a_{n} = a_{1}r^{n-1}$. 

Then solving for $a_{1}$ in both equations and setting them equal to one another, 
$$\frac{162}{r^{4}} = \frac{-4374}{r^{7}}$$

You can then solve for $r$ (your common ratio), and subsequently $a_{1}$ (your first term). You then have all of the information you need.
I had a similar question and tried to solve it alone i used this way 

since the initial value is f(1) so u use this equation f(n) = ar^n-1

since u have f(5) as initial value or actually (known value) then we have to change it to this 

f(n) = a5 * r (n-5)  , so we know that the 8 th term f(8) = -4734 
so :  f(8) = a5 * r(8-5)   and f(5)= 162

-4734 = 162 *r^3

-47324/162 = r^3 

r^3 = -27 then calculate ......