Mathematics

A geometric progression multiplies by the same factor each step, so the ratio between any two terms depends only on how many steps apart they are. Since you know two terms and their positions, you can set up an equation using the relationship $a_n = a_1 \cdot r^{n-1}$ — or more directly, notice that going from term 3 to term 6 is exactly 3 steps, so the 6th term equals the 3rd term times $r^3$. Use this to find $r$ without needing to find $a_1$ first.

A geometric progression multiplies by the same factor each step, so the ratio between any two terms depends only on how many steps apart they are. Since you know two terms and their positions, you can set up an equation using the relationship $a_n = a_1 \cdot r^{n-1}$ — or more directly, notice that going from term 3 to term 6 is exactly 3 steps, so the 6th term equals the 3rd term times $r^3$. Use this to find $r$ without needing to find $a_1$ first.