CONTINUED PROPORTION
Three quantities x, y, z are said to be in "CONTINUED PROPORTION” if x : y = y : z.
The three quantities must be of the “SAME KIND”. The quantity ‘y’ is called the “MEAN PROPORTIONAL” between x & z, while the quantity z is called the “THIRD PROPORTIONAL” to x & y.
x y
Now, if ---------- = ---------- then y² = xz
y z
Hence we can find y = √ xz, x = y²/ z and z = y²/ x
For your better understanding, we are introducing some example -
Example.1) The numbers 4, 12 & 36 are in continued proportion because
4 1
4 : 12 = ----------- = ----------- = 1 : 3
12 3
12 1
12 : 36 = ----------- = ---------- = 1 : 3
36 3