Question

If 6x²y, 12xy², z are in continued proportion then find the value of z.​

Answer 1

Answer:

24y³

Step-by-step explanation:

Since 6x²y , 12xy² , and z are in continued proportion then

6x²y : 12xy² :: 12xy² : z

if a : b  = b : c  i.e. a/b = b/c i.e. b² = ac

if a , b , c are in continuous proportion then the middle term b is called the mean proportion between 'a' and 'c' , 'a' is the first proportion and 'c' is the third proportion

Thus , if b is the mean proportion between 'a' and 'c'

then b² = ac i.e. b = √(ac)

⇒ (12xy²)² = 6x²y × z

z = (12xy²)² ÷ 6x²y

z = 24y³

Hence the Third term term = 24y³