Question

Find the four arithmetic means between -21 and -36. Show work.

Answer 1

Please read the answers below.

Explanation:

Let's calculate the four means between -21 and -36, this way:

1. Arithmetic mean:

(-21 + -36)/2 = -57/2 = -28.5

2. Weighted mean:

We will assign equal weight to both numbers : 5

(-21 * 5 + -36 * 5)/10 = (-105 + -180)/10 = -285/10 = -28.5

3. Geometric mean:

√-21 * -36 = √756 = 27.5 (Rounding to the next tenth)

4. Harmonic mean:

2/(1/-21 + 1/-36) = 2/(-0.0476 + -0.0277) = -26.6 (Rounding to the next tenth)

Answer 2

Answer: - 24 , - 27 , - 30 , - 33

Explanation:

Let the arithmetic means be p , q , r , s. The sequence then becomes :

-21 , p , q , r , s , -36

where :

The first term (a ) = - 21

common difference(d ) = ?

number of terms (n ) = 6

Last term (L) = -36

We will use the formula ; L = a + (n - 1 ) d to find the value of d , that is

- 36 = - 21 + ( 6 - 1 ) d

-36 + 21 = 5d

- 15 = 5d

Therefore :

d = -3

we will then use the value of d to find p , q , r and s.

p is the second term , that is

p = a + d

p = -21 + (-3)

p = -21 - 3

p = -24

q = a + 2d

q = - 21 +2(-3)

q = -27

r = a + 3d

r = - 21 + 3 (-3)

r = -30

s = a+ 4d

s = - 21 + 4 ( -3 )

s = -33

Therefore : the arithmetic means are ; - 24 , - 27 , - 30 , - 33