Question

Find the three arithmetic means between 10 and 18

Answer 1

The answer is 12, 14, 16

Answer 2

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

`a=10`

and

`a+(5-1)d=18\\\\ \Rightarrow 10+4d=18\\\\ \Rightarrow 4d=18-10\\\\ \Rightarrow 4d=8\\\\ \Rightarrow d=(8)/(4)\\\\ \Rightarrow d=2.`

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.