Hi please i need the complete step-by-step solution thank you

9, 16, 23, 30

Step-by-step explanation:

The arithmetic means are the terms of an arithmetic sequence, that is

2, a₂, a₃, a₄, a₅, 37

The nth term of the sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and a₆ = 37 , that is

a₁ + 5d = 37

2 + 5d = 37 ( subtract 2 from both sides )

5d = 35 ( divide both sides by 5 )

d = 7

Then

a₂ = a₁ + 7 = 2 + 7 = 9

a₃ = a₂ + 7 = 9 + 7 = 16

a₄ = a₃ + 7 = 16 + 7 = 23

a₅ = a₄ + 7 = 23 + 7 = 30

The 4 arithmetic means between 2 and 37 are 9, 16, 23, 30