To find: Six arithmetic means between 11 and -10

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

n is the number of arithmetic means

(ii) A_n = a + nd

We have 11 and -10

Using Formula,

Using Formula, A_n = a + nd

First arithmetic mean, A₁ = a + d

= 11 + (-3)

= 8

Second arithmetic mean, A₂ = a + 2d

= 11 + 2(-3)

= 11 + (-6)

= 5

Third arithmetic mean, A₃ = a + 3d

= 11 + 3(-3)

= 11 + (-9)

= 2

Fourth arithmetic mean, A₄ = a + 4d

= 11 + 4(-3)

= 11 + (-12)

= -1

Fifth arithmetic mean, A₅ = a + 5d

= 11 + 5(-3)

= 11 + (-15)

= -4

Sixth arithmetic mean, A₆ = a + 6d

= 11 + 6(-3)

= 11 + (-18)

= -7

Ans) The six arithmetic means between 11 and -10 are 8, 5, 2, - 1, -4 and -7.