Find common ratio with two terms

Question

I am trying to find common ratio but ...

If $b_1 = -2$ and $b_8 = -384$, how can I find common ratio (q)?

Answer 1

The fact that you're asking for a common ratio probably means that the sequence with terms $b_n$ form a geometric sequence but that's something you should mention. It also helps to show your own effort, ideas or relevant formulas you have seen.

You probably know that $b_n = q \cdot b_{n-1}$ and from this also $b_n = q^{n-1}\cdot b_1$. You know $b_1$ and $b_8$ so use this formula with $n=8$ to get an equation for $q$.

Answer 2

Hint:

For a geometric progression with first term $a$ and common ratio $r$, the $n^{\text{th}} $ term is given by: $$b_n = ar^{n-1}$$

Here, $b_1 =a=-2$ and $b_8 = - 384$.

Can you take it from here?

Answer 3

Hint: $b_n = b_0 q^{n}$. Compute $b_8 / b_1$.