Answer:
96, 84, 72, 60, 48, 36
Step-by-step explanation:
The 6 arithmetic means are the terms of an arithmetic sequence between 108 and 24
let the means be a, b, c, d, e, f , then sequence is
108, a, b, c, d, e, f, 24
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 108 , and n = 8
24 = 108 + 7d ( subtract 108 from both sides )
- 84 = 7d ( divide both sides by 7 )
- 12 = d
Then
a = 108 - 12 = 96
b = 96 - 12 = 84
c = 84 - 12 = 72
d = 72 - 12 = 60
e = 60 - 12 = 48
f = 48 - 12 = 36
The 6 arithmetic means are 96, 84, 72, 60, 48, 36
