# 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.

• @Lindsay If you ever return to Math Stack Exchange, note that you can accept any single answer you find most helpful by selecting the green checkmark beside that answer. Of course you don't have to accept any answer if you don't want to! Jul 9, 2015 at 16:42

If $ar^4 = 162$ and $ar^7 = 4374$ then $$\frac{-4374}{162} = \frac{ar^7}{ar^4} = r^3$$ so $$r^3 = \frac{-4374}{162} = -27.$$ If you know $r^3=-27$ can you find $r$? If you know $r$ and $ar^4$ can you find $a$?

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 ......