The problem states that we have three numbers in an arithmetic progression (A.P.) and their product is 224. It also states that the largest number is 7 times the smallest.

Let's denote the three numbers as follows:
- The smallest number is x.
- The middle number is x + d, where d is the common difference in the A.P.
- The largest number is x + 2d.

According to the problem, the largest number is 7 times the smallest, so we can write the equation:
x + 2d = 7x.

Solving this equation for d gives us:
d = 3x.

The product of the three numbers is 224, so we can write the equation:
x * (x + d) * (x + 2d) = 224.

Substituting d = 3x into this equation gives us:
x * (x + 3x) * (x + 6x) = 224,
which simplifies to:
x^3 * 10 = 224.

Solving this equation for x gives us:
x^3 = 22.4,
and taking the cube root of both sides gives us:
x = 2.82 (approximately).

So, the smallest number is approximately 2.82.

Question

The problem states that we have three numbers in an arithmetic progression (A.P.) and their product is 224. It also states that the largest number is 7 times the smallest.

Let's denote the three numbers as follows: 
- The smallest number is x.
- The middle number is x + d, where d is the common difference in the A.P.
- The largest number is x + 2d.

According to the problem, the largest number is 7 times the smallest, so we can write the equation: 
x + 2d = 7x.

Solving this equation for d gives us: 
d = 3x.

The product of the three numbers is 224, so we can write the equation: 
x * (x + d) * (x + 2d) = 224.

Substituting d = 3x into this equation gives us: 
x * (x + 3x) * (x + 6x) = 224,
which simplifies to: 
x^3 * 10 = 224.

Solving this equation for x gives us: 
x^3 = 22.4,
and taking the cube root of both sides gives us: 
x = 2.82 (approximately).

So, the smallest number is approximately 2.82.

Knowee AI · Accepted Answer

The problem states that we have three numbers in an arithmetic progression (A.P.) and their product is 224. It also states that the largest number is 7 times the smallest.

Let's denote the three numbers as follows: 
- The smallest number is x.
- The middle number is x + d, where d is the common difference in the A.P.
- The largest number is x + 2d.

According to the problem, the largest number is 7 times the smallest, so we can write the equation: 
x + 2d = 7x.

Solving this equation for d gives us: 
d = 3x.

The product of the three numbers is 224, so we can write the equation: 
x * (x + d) * (x + 2d) = 224.

Substituting d = 3x into this equation gives us: 
x * (x + 3x) * (x + 6x) = 224,
which simplifies to: 
x^3 * 10 = 224.

Solving this equation for x gives us: 
x^3 = 22.4,
and taking the cube root of both sides gives us: 
x = 2.82 (approximately).

So, the smallest number is approximately 2.82.

The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the smallest number.Answer( Please choose a correct answer ) CLEAR2347

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