To find: Three arithmetic means between 23 and 7

Formula used: (i) , where, d is the common difference

n is the number of arithmetic means

(ii) A_n = a + nd

We have 23 and 7

Using Formula,

Using Formula, A_n = a + nd

First arithmetic mean, A₁ = a + d

= 23 + (-4)

= 19

Second arithmetic mean, A₂ = a + 2d

= 23 + 2(-4)

= 23 + (-8)

= 15

Third arithmetic mean, A₃ = a + 3d

= 23 + 3(-4)

= 23 + (-12)

= 11

Ans) The three arithmetic means between 23 and 7 are 19, 15 and 11