We should think about the three numbers in A.P. as
![\[\mathbf{a}\text{ }\text{ }\mathbf{d},\text{ }\mathbf{a},\text{ }\mathbf{and}\text{ }\mathbf{a}\text{ }+\text{ }\mathbf{d}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a648d84f29c451ebdae9beb0fc5ac15c_l3.png "Rendered by QuickLaTeX.com")
Then, at that point, from the inquiry we have
![\[\left( \mathbf{a}\text{ }\text{ }\mathbf{d} \right)\text{ }+\text{ }\left( \mathbf{a} \right)\text{ }+\text{ }\left( \mathbf{a}\text{ }+\text{ }\mathbf{d} \right)\text{ }=\text{ }\mathbf{24}\text{ }\ldots \text{ }\left( \mathbf{I} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-59714d28abd259aad819eb4e2a95bb1a_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{3a}\text{ }=\text{ }\mathbf{24}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e13a2bbb3ffc7014d4f7ab63c8660f4a_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore \mathbf{a}\text{ }=\text{ }\mathbf{8}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-87f29fb5ebd934a829d6a9e866a94060_l3.png "Rendered by QuickLaTeX.com")
Also,
![\[\left( \mathbf{a}\text{ }\text{ }\mathbf{d} \right)\text{ }\left( \mathbf{a}\text{ }+\text{ }\mathbf{d} \right)\text{ }=\text{ }\mathbf{440}\text{ }\ldots \text{ }\left( \mathbf{ii} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0f394542eb25718ba4251a6c3db46f57_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{8}\text{ }\text{ }\mathbf{d} \right)\text{ }\left( \mathbf{8} \right)\text{ }\left( \mathbf{8}\text{ }+\text{ }\mathbf{d} \right)\text{ }=\text{ }\mathbf{440}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8ea95bebd31f88d5dcf51f45d111ba25_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{8}\text{ }\text{ }\mathbf{d} \right)\text{ }\left( \mathbf{8}\text{ }+\text{ }\mathbf{d} \right)\text{ }=\text{ }\mathbf{55}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-69a2624b177a24b44352e5da9e473b40_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{64}\text{ }\text{ }\mathbf{d2}\text{ }=\text{ }\mathbf{55}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-93d8c55e85dc9224bfc83c8c4dd94315_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{d2}\text{ }=\text{ }\mathbf{64}\text{ }\text{ }\mathbf{55}\text{ }=\text{ }\mathbf{9}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f56df1a404320102613e5d75be2e0393_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore \mathbf{d}\text{ }=\text{ }\pm \text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-74176d826143795e74aee5cd0749c4f6_l3.png "Rendered by QuickLaTeX.com")
In this way,
At the point when
![\[\mathbf{d}\text{ }=\text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56e5142bc68c8eb1bf29c4834abfc866_l3.png "Rendered by QuickLaTeX.com")
, the numbers are
![\[\mathbf{5},\text{ }\mathbf{8},\text{ }\mathbf{and}\text{ }\mathbf{11}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-37ec9f5a5a05d4aca4b4feb0d6119ea5_l3.png "Rendered by QuickLaTeX.com")
and
At the point when
![\[\mathbf{d}\text{ }=\text{ }\text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d77a20d62492f5f3a12fb0ac4d945031_l3.png "Rendered by QuickLaTeX.com")
, the numbers are
![\[\mathbf{11},\text{ }\mathbf{8},\text{ }\mathbf{and}\text{ }\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b022b6ab8d6ca326304db25e620e4f06_l3.png "Rendered by QuickLaTeX.com")
.
In this way, the three numbers are
.