Insert six arithmetic means between 11 and -10.

1.	Insert six arithmetic means between 11 and -10.
Answer» To find: Six arithmetic means between 11 and -10 Formula used: (i) d = b-a/n+1, 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, d = b-a/n+1 d = -10-(11)/6+1 = -21/7 = -3 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.

Answer»

To find: Six arithmetic means between 11 and -10

Formula used: (i) d = b-a/n+1, 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, d = b-a/n+1

d = -10-(11)/6+1 = -21/7 = -3

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.

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