Fill up the empty cells of the square below such that the numbers in each row and column from arithmetic sequences:

What if we use other numbers instead of 1, 4 28 and 7?

For 1^st row,

a = 1 a₄ = 4

a₄ = a + 3d

∴ d = 1

a₂ = 1 + 1 = 2

∴ A₁₂ = 2

a₃ = 2 + 1 = 3

∴ A₁₃ = 3

For 1^st column,

a = 1 a₄ = 7

a₄ = a + 3d

∴ d = 2

a₂ = 1 + 2 = 3

∴ A₂₁ = 3

a₃ = 3 + 2 = 5

∴ A₃₁ = 5

For 4^th row,

a = 7 a₄ = 28

a₄ = a + 3d

∴ d = 7

a₂ = 7 + 7 = 14

∴ A₄₂ = 14

a₃ = 14 + 7 = 21

∴ A₄₃ = 21

For 4^th column,

a = 4 a₄ = 28

a₄ = a + 3d

∴ d = 8

a₂ = 4 + 8 = 12 ∴ A₂₄ = 12

a₃ = 12 + 8 = 20 ∴ A₃₄ = 20

For 2^nd row,

a = 3 a₄ = 12

a₄ = a + 3d

∴ d = 3

a₂ = 3 + 3 = 6 ∴ A₄₂ = 6

a₃ = 6 + 3 = 9 ∴A₂₃ = 9

For 3^rd row,

a = 5 a₄ = 20

a₄ = a + 3d

∴ d = 5

a₂ = 5 + 5 = 10

∴ A₃₂ = 10

a₃ = 10 + 5 = 15

∴ A₃₃ = 15

If we use numbers other than 1,4,7,and 28 it is not guaranteed that the grid will be completely filled such that each row and column is in AP.