Question

When a, b, c are in cotinued proportion then b is known as ____________ of a and c or mean proportional of a and c.​

Answer 1

. a, b and c are in continued proportion, if a : b = b : c

The second quantity is called the mean proportional between the first and the third

i.e. in a : b = b : c; b is the mean proportional between a and c.

The third quantity is called the third proportional to the first and the second

i.e. in a : b = b : c; c is the third proportional to a and b.

Answer 2

Answer: Geometric Mean

Step-by-step explanation:  When a, b, c are in continued proportion then b is known as Geometric mean of a and c or mean proportional of a and c.

If a , b , c  are in continued proportion We can say that,

a:b = b:c

or,

a/b = b/c

b × b = ac

b² = ac

b =  √ac

Also,

Series:- a, b , c..... known as  the geometric  series. These terms has  a common ratio.

For example,

2 , 4 , 8 , 16 , 32 ....... are  in Geometric Progression(GP) because,

4/2 = 8/4 = 16/8 = 32/16 ....... = 2