Question

In a continued propotion, the first term is x^3yand 2nd is x^2 y^2 then the 3rd one is?
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Answer 1

Answer:

1st term is x³y

2nd term is. x²y²

then third term is. xy³

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Answer 2

Step-by-step explanation:

Given:-

In a continued propotion, the first term is

x^3yand 2nd is x^2 y^2 .

To find:-

Find the third term ?

Solution:-

Given taht :

First term in the continued proportion = x^3y

Second term in the continued Proportion = x^2y^2

Let the third term be A

Now ,since they are in continued proportion

=>x^3y : x^2y^2::x^2y^2:A

Product of extremes = x^3y ×A

Product of means = (x^2y^2)×(x^2y^2)

We know that

Product of extremes = Product of means

=>x^3y× A = (x^2y^2)×(x^2y^2)

=>A = (x^2y^2)×(x^2y^2)/(x^3y)

=>A = x^(2+2)y^(2+2)/x^3y

since a^m ×a^n = a^(m+n)

=>A= x^4y^4/x^3y

=>A = x^(4-3)×y^(4-1)

Since a^m/a^n = a^(m-n)

=>A = x^1y^3

=>A = xy^3

The third term = xy^3

Answer:-

The third term in the given Proportion is xy^3

Used formulae:-

• In proportion, Product of means = Product of extremes
• a^m/a^n = a^(m-n)
• a^m ×a^n = a^(m+n)