Answer:

1. -9, __, 11

An = A1 + d(n-1)

11 = -9 + d(3-1)

20 = d2

d = 10

Then -9 + 10 = 1

So the arithmetic mean is 1

2. 1/4, __, __, 1

An = A1 + d(n-1)

1 = 1/4 + d(4-1)

3/4 = d3

d = 3/12

d = 1/4

Then 1/4 +1/4 = 1/2, and 1/2 + 1/4 = 3/4

So the two arithmetic means are 1/2 and 3/4

3. 7, __, __, __, 63

An = A1 + d(n-1)

63 = 7 + d(5-1)

56 = d4

d= 14

Then 7+14 = 21, 21+14 = 35, and 35+14 = 49

So the three arithmetic means are 21, 35, and 49

4. 3a+b, __, __, 6a+7b

An = A1 + d(n-1)

6a+7b = 3a+b + d(4-1)

3a+6b = d(3)

d = a+2b

Then 3a+b + a+2b = 4a+3b, 4a+3b + a+2b = 5a+5b

So the two arithmetic means are 4a+3b and 5a+5b

5. -x, __, __, __, __, __, 17x

An = A1 + d(n-1)

17x = -x + d(7-1)

18x = d(6)

d = 3x

Then -x+3x = 2x, 2x+3x = 5x, 5x+3x = 8x, 8x+3x = 11x, and 11x+3x= 14x

So the five arithmetic means are 2x, 5x, 8x, 11x, and 14x