Question Type 2: Finding the common ratio given two terms Exercises

For a geometric sequence, $u_2 = 10$ and $u_3 = 25$. Find the common ratio $r$.

In a geometric sequence, $u_3 = 12$ and $u_6 = 96$. Find the common ratio $r$.

Given a geometric sequence with $u_3 = -16$ and $u_5 = -256$, find all possible values of $r$.

A geometric sequence has terms $u_1 = -3$ and $u_4 = -24$. Find the common ratio $r$.

A geometric sequence satisfies $u_6 = 64$ and $u_9 = 512$. Find the common ratio $r$.

Given a geometric sequence of positive terms with $u_4 = 162$ and $u_8 = 2$, find the common ratio $r$.

Given $u_4 = 8$ and $u_{10} = 512$ in a geometric sequence with positive terms, find the common ratio $r$.

A geometric sequence has $u_3 = 50$ and $u_4 = 37.5$. Find the common ratio $r$.

A geometric sequence has first term $u_1 = 2$ and fourth term $u_4 = 16$. Find the common ratio $r$.

In a geometric sequence, $u_2 = 5$ and $u_5 = 40$. Find the common ratio $r$.

Given a geometric progression where $u_2 = 8$ and $u_5 = 1$, find the common ratio $r$.

In a geometric sequence, $u_4 = 81$ and $u_6 = 729$. Find all possible values of the common ratio $r$.

In a geometric sequence with a positive common ratio, $u_3 = 4$ and $u_7 = 256$. Determine the exact value of the common ratio $r$.

In a geometric sequence the first three terms are $81$, $27$, and $9$. Determine the common ratio $r$ and the sixth term.

Given a geometric sequence with $u_2 = 18$ and $u_5 = 486$, find the common ratio $r$.

In a geometric sequence, $u_5 = 243$ and $u_8 = 6561$. Determine $r$.