# The consecutive terms of a geometric progression

Three consecutive terms of a geometric progression

If e, f and g are 3 consecutive terms of GP, then

$g f = f e$

Example

If $p+20,\text{\hspace{0.17em}}\text{ }\text{ }p-4,\text{\hspace{0.17em}}\text{ }\text{ }\text{ }p-20$   are three consecutive terms of a geometric progression, find the value of p.

Solution

$\frac{p-20}{p-4}=\frac{p-4}{p+20}$

$\begin{array}{l}\\ p=52\end{array}$