Answer: The three arithmetic means between 10 and 18 are 12, 14 and 16.
Step-by-step explanation: We are given to find three arithmetic means between 10 and 18.
Let a+d, a+2d and a+3d be the three arithmetic means between 10 and 18.
Then, 10, a+d, a+2d, a+3d and 18 will form an arithmetic sequence with first term 10 and 5th term 18.
So, we have
[tex]a=10[/tex]
and
[tex]a+(5-1)d=18\\\\ \Rightarrow 10+4d=18\\\\ \Rightarrow 4d=18-10\\\\ \Rightarrow 4d=8\\\\ \Rightarrow d=\dfrac{8}{4}\\\\ \Rightarrow d=2.[/tex]
Therefore, we get
a+d = 10 + 2 = 12.
a+2d = 10 + 2×2 = 10 + 4 = 14
and
a+3d = 10 + 3×2 = 10 + 6 = 16.
Thus, the three arithmetic means between 10 and 18 are 12, 14 and 16.
