#### What is Continued Proportion?

Three numbers are said to be in Continued Proportion if the ratio of first and second number is equal to the ratio of second and third number.

If three numbers a, b, c are in continued proportion

Then,

**a : b : : b : c**

**Example 1**

If 48, 24, a are in continued proportion, find the value of a?

**Explanation:**

Given – 48 , 24 , a are in continued proportion.

So,

48 : 24 :: 24 : a

(Product of extremes = Product of means)

Here, Extremes are 48 and a

Means are 24 and 24

48 x a = 24 x 24

Now, on simplifying we get a = = 12

Hence, the value of ‘a’ is 12

**Example 2**

If 12, 42, a are in continued proportion, find the value of a?

**Explanation:**

Given – 12 , 42 , a are in continued proportion.

So,

12 : 42 :: 42 : a

(Product of extremes = Product of means)

Here, Extremes are 12 and a

Means are 42 and 42

12 x a = 42 x 42

Now, on simplifying we get a = = 147

Hence, the value of ‘a’ is 147

**Example 3**

If 28, 14, a are in continued proportion, find the value of a?

**Explanation:**

Given – 28 , 14 , a are in continued proportion.

So,

28 : 14 :: 14 : a

(Product of extremes = Product of means)

Here, Extremes are 28 and a

Means are 14 and 14

28 x a = 14 x 14

Now, on simplifying we get a = = 7

Hence, the value of ‘a’ is 7

**Example 4**

If 48, 12, a are in continued proportion, find the value of a?

**Explanation:**

Given – 48 , 12 , a are in continued proportion.

So,

48 : 12 :: 12 : a

(Product of extremes = Product of means)

Here, Extremes are 48 and a

Means are 12 and 12

48 x a = 12 x 12

Now, on simplifying we get a = = 3

Hence, the value of ‘a’ is 3

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