Useful tricks:

• For 3 terms in GP, assume a/r, a, ar (product = $a^3$)
• For 4 terms in GP, assume a/$r^3$, a/r, ar, $ar^3$ (common ratio = $r^2$)
• Product of n terms of GP: P = ($a_1$ * $a_n$)^{n/2} = $a^n$ * r^{n$\frac{n-1}{2}$}
• If each term is multiplied by a constant, the sequence is still GP
• Sum of infinite GP converges iff |r| < 1
• r = (any term) / (preceding term)