
Divide 24 in three parts such that they are in AP and their product is 440.
Answer
461.1k+ views
Hint:
As given in the question the three parts are in AP then let the three parts of 24 is $a - d, a, a + d$. Then submission of all three parts is equal to 24 from here we will calculate a. then the product of three parts is 440 from this we will calculate d.
Complete step by step solution:
Given three parts of 24 is in AP then let us assume three numbers to be $a - d, a, a + d$
So, $a - d + a + a + d = 24$
Therefore $a = 8$
Now, product of all three parts are 440 then
$\left( {a - d} \right) \times \left( a \right) \times \left( {a + d} \right) = 440$
Substituting $a = 8$
$\left( {8 - d} \right) \times \left( 8 \right) \times \left( {8 + d} \right) = 440$
We know that ${a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right)$
\[\left( {{8^2} - {d^2}} \right) = 55\]
${d^2} = 64 - 55 = 9$
Taking root on both side we get
$d = 3$
So, three parts of 24 are 5, 8, 11.
Note:
For consecutive three terms to be in AP $a - d,a,a + d$
For 4 consecutive terms in AP =$a - 2d,a - d,a + d,a + 2d$ and so one …
Where a is the 1st term of AP and d is the common difference
As given in the question the three parts are in AP then let the three parts of 24 is $a - d, a, a + d$. Then submission of all three parts is equal to 24 from here we will calculate a. then the product of three parts is 440 from this we will calculate d.
Complete step by step solution:
Given three parts of 24 is in AP then let us assume three numbers to be $a - d, a, a + d$
So, $a - d + a + a + d = 24$
Therefore $a = 8$
Now, product of all three parts are 440 then
$\left( {a - d} \right) \times \left( a \right) \times \left( {a + d} \right) = 440$
Substituting $a = 8$
$\left( {8 - d} \right) \times \left( 8 \right) \times \left( {8 + d} \right) = 440$
We know that ${a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right)$
\[\left( {{8^2} - {d^2}} \right) = 55\]
${d^2} = 64 - 55 = 9$
Taking root on both side we get
$d = 3$
So, three parts of 24 are 5, 8, 11.
Note:
For consecutive three terms to be in AP $a - d,a,a + d$
For 4 consecutive terms in AP =$a - 2d,a - d,a + d,a + 2d$ and so one …
Where a is the 1st term of AP and d is the common difference
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
Define least count of vernier callipers How do you class 11 physics CBSE

The combining capacity of an element is known as i class 11 chemistry CBSE

Proton was discovered by A Thomson B Rutherford C Chadwick class 11 chemistry CBSE

Find the image of the point 38 about the line x+3y class 11 maths CBSE

Can anyone list 10 advantages and disadvantages of friction

Distinguish between Mitosis and Meiosis class 11 biology CBSE
