Ответ:

d = 3

Объяснение:

Формулы арифметической прогрессии:
Sₙ = n*(a₁ + aₙ)/2;   aₙ = а₁ + d(n – 1).

1) S₁₀ = 10(a₁ + a₁₀)/2

   225 =10(9 + a₁₀)/2 = 5(9 + a₁₀)

   45 = 9 + a₁₀

   a₁₀ = 45 - 9
  a₁₀ = 36

2)  a₁₀ = a₁ + d(10-1) = a₁ +9d

9d = a₁₀ - a₁

d = (a₁₀ - a₁)/9

d = (36 - 9)/9 = 27/9

d = 3

[tex]\displaystyle\bf\\a_{1}= 9\\\\S_{10} =225\\\\d=?\\\\\\S_{10} =\frac{2a_{1} +9d}{2} \cdot 10=(2a_{1} +9d)\cdot 5\\\\\\225=(2\cdot 9+9d)\cdot 5\\\\\\45=18+9d\\\\\\9d=27\\\\\\\boxed{d=3}[/tex]