Question

Divide 21 into three parts in A.P such that the product of the first and second parts is 21.

Answer 1

3,7,11...is the required A.P.

with common difference 4

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Answer 2

The required AP is 3, 7, 11.

Step-by-step explanation:

We need to divide 21 into three parts in A.P such that the product of the first and second parts is 21.

Let the three parts of AP are a-d, a, a+d.

Sum of these terms is 21.

$(a-d)+a+(a+d)=21$

$3a=21$

Divide both sides by 3.

$a=7$

The value of a is 7.

Product of the first and second parts is 21.

$(a-d)a=21$

$a^2-da=21$

Substitute a=7 in the above equation.

$7^2-7d=21$

$49-7d=21$

$49-21=7d$

$28=7d$

Divide both sides by 7.

$4=d$

The value of d is 4. Therefore, the required AP is 3, 7, 11.

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