Question

30 points! Find the four arithmetic means between -17 and 32.

Answer 1

Answer: - 7.2 , 2.6 , 12.4 and 22.2

Step-by-step explanation:

Let the arithmetic means be p , q , r ,s , therefore , the sequence becomes:

-17 , p , q , r , s , 32

The first term (a ) = -17

Last term (L) = 32

common difference (d) = ?

number of terms (n ) = 6

We will use the formula for calculating the last term to find the common difference. That  is

L = a + (n - 1 ) d

Substituting the values , we have

32 = -17 + (6-1) d

32 = -17 + 5d

32 + 17 = 5d

49 = 5d

Therefore: d = 9.8

We can therefore find the values of p , q , r , and s

p is the second term , that is

p = a + d

p = -17 + 9.8

p = -7.2

q = a + 2d

q = - 17 + 19.6

q = 2.6

r = a + 3d

r = - 17 + 29.4

r = 12.4

s = a + 4d

s = - 17 + 39.2

s = 22.2

Therefore : the arithmetic means are : - 7.2 , 2.6 , 12.4 and 22.2