Answer:
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
[tex]a_{n}[/tex] = 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
