Question

In an AP sum of 3 terms is 24 and their product is 480 . Find the three terms

Answer 1

Let the numbers be a-d, a and a+d

According to first condition,

a - d + a + a + d = 24

=> 3a = 24

=> a = 8


According to second condition,

( a - d) (a) (a +d) = 504

=> a ( a^2 - d^2) = 504

=> 8 [ (8)^2 - (d)^2] = 504

=> 64 - d^2 = 63

=> d^2 = 1

=> d = 1

First number = 8 - 1 = 7

Second number = 8

Third number = 8 +1 = 9

Answer 2

The three terms of AP are 6, 8, and 10 or 10, 8, and 6.

Given:

An AP sum of three terms is 24 and their product is 480.

To Find:

The three terms.

Solution:

Let's suppose the three terms of an AP as $a-d,$ $a$ and $a+d.$

It is given that the sum of these three terms is $24$.

now, we get,

$(a-d)+a+(a+d)=24$.

or,

$a=8$

It is given that the product of these terms is 480.

here, we get,

$(8-d)\times 8\times (8+d)=480.$

now, after solving the above equation.

we get,

$(8-d)(8+d)=60\\64-d^{2} =60\\d=\pm 2$

we get the value of $=-2$ or $+2$.

By putting the value  $d$ in the given terms.

The three terms of $AP$ will be $6, 8$ and $10$ or $10,8$ and $6.$

Hence, the three terms of AP are 6, 8, and 10 or 10, 8, and 6.

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