Divide 24 in three parts such that they are in AP and their product is 440.

Let the required parts of 24 be (a - d), a and (a + d) such that they are in AP. 
Then (a - d) + a + (a + d) = 24
⇒ 3a = 24  
⇒ a = 8​
Also, (a - d).a.(a + d)​ = 440

$\Rightarrow a\left(a^{2}-d^{2}\right)=440$

$\Rightarrow 8\left(64-d^{2}\right)=440$

$\Rightarrow d^{2}=64-55=9$

$\Rightarrow d=\pm 3$

Thus, $a=8$ and $d=\pm 3$

 Hence, the required parts of 24 are (5, 8,11) or (11, 8, 5).