Question

The sum of three numbers of an A P is 18 and their product is 280. Find the numbers.

Answer 1

let the other no. be x
18*x= 280
x=280/18
x=15.55556

Answer 2

The numbers are 4, 7 and 10.

*Correct question is:

Given:

• The sum of three numbers of an A.P. is 21 and
• The product of numbers are 280.

To find:

• Find the numbers.

Solution:

Concept to be used:

• When three numbers are to be assumed, these must be a-d, a, and a+d.

Step 1:

Find the value of 'a'.

The sum of three numbers = 21, so write the equation.

$a - d + a + a + d = 21$

$3a = 21$

$a = \frac{21}{3}$

$\bf a = 7$

Step 2:

Find the value of 'd'.

The product of numbers are 280.

$(a - d) \times a \times (a + d) = 280$

$a( {a}^{2} - {d}^{2} ) = 280$

$\because\:(x-y) (x+y) = {x}^{2} - {y}^{2}$

$7(49 - {d}^{2} ) = 280$

$49 - {d}^{2} = \frac{280}{7}$

$49 - {d}^{2} = 40$

$- {d}^{2} = - 9$

${d}^{2} = 9$

$\bf d = \pm3$

Step 3:

Find the numbers.

First number is $7 - 3 = 4$

Second number is 7

and third number is $7 + 3 = 10$

or vice versa, if taking d= -3.

Thus,

The numbers are 4, 7 and 10.

Learn more:

1) If the sum of the first 8 terms of AP is 136 and that of first 15 terms is 465 then find the sum of first 25 terms

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2) For what value of k, 2k-7 , k+5 and 3k+2 are three consecutive terms of an A.P ?

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