Find the four arthmetic means between - 3 and 46

The arithmetic means are

6.8, 16.6, 26.4 and 36.2

Step-by-step explanation:

Let the four terms be w, x, y and z.

In an arithmetic sequence, each consecutive term differs by a common difference, d.

First term = - 3

Second term, w = a + d = - 3 + d

Third term, x = a + 2d = - 3 + 2d

Fourth term, y = a + 3d = - 3 + 3d

Fourth term = a + 4d = - 3 + 4d

Last term = a + 5d = - 3 + 5d

Since the last term is 46, it means that

- 3 + 5d = 46

5d = 46 + 3 = 49

d = 49/5 = 9.8

Therefore,

w = - 3 + 9.8 = 6.8

x = - 3 + 2 * 9.8 = - 3 + 19.6 = 16.6

y = - 3 + 3 * 9.8 = - 3 + 29.4 = 26.4

z = - 3 + 4 * 9.8 = - 3 + 39.2 = 36.2

6.8, 16.6, 26.4, 36.2

Step-by-step explanation:

Let's write the sequence, d is the common difference:

- 3, - 3 + d, - 3 + 2d, - 3 + 3d, - 3 + 4d, 46

Therefore 46 = - 3 + 5d

5d = 49

d = 49/5 = 9.8

So the first arithmetic mean is - 3 + 9.8 = 6.8. and the second is - 3 + 2 (9.8) = 16.6 ...

They are:

6.8, 16.6, 26.4, 36.2.