IB Mathematics Analysis and Approaches 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 $r$.