If 20 divided into four parts which are in AP such that the product of the first and fourth is to the products of the second and third is in the radio 2 : 3?

Let the four parts be (a - 3d), (a - d), (a +d), (a + 3d).
From question,
(a -3d) + (a - d) + (a + b) + (a + 3d) = 20
⇒ a = 5
Also, [(a - 3d) (a +3d)] / [(a - d) (a + d)] = 2/3
⇒ [a² - 9d²] / [a² - d²] = 2/3
⇒ [5² - 9d²] / [5² - d²] = 2/3
⇒ d = 1
∴ a = 5, d = 1
So, the four parts are 2, 4, 6, 8