Question

Find the four arithmetic means between 100 and 135. Show work.

Answer 1

Answer: 107 , 114 , 121 , 128

Step-by-step explanation:

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

100 , p, q , r , s , 135

This means that there are 6 terms in all.

first term (a) = 100

last term (l) = 135

common difference (d) = ?

The formula for finding the Last term is given by

L = a + (n - 1 ) d

substituting each values , we have

135 = 100 + ( 6 - 1 ) d

135 = 100 + 5d

135 - 100 = 5d

35 = 5d

Therefore: d = 7

Since we know the value of d , we can find the arithmetic mean between 100 and 135.

p is the second term , and second term is calculated by $t_{2}$ = a + d

Therefore:

p = a + d

p = 100 + 7

p = 107

q = a + 2d

q = 100 + 14

q = 114

r = a + 3d

r = 100 + 21

r = 121

s = a + 4d

s = 100 + 28

s = 128

Therefore : the arithmetic means between 100 and 135 are 107, 114 , 121 and 128

Answer 2

Answer:

Please read the answers below.

Step-by-step explanation:

Let's calculate the four means between 100 and 135, this way:

1. Arithmetic mean:

(100 + 135)/2 = 117.5

2. Weighted mean:

We will assign equal weight to both numbers : 5

(100 * 5 + 135 * 5)/10 = (500 + 675)/10 = 1,175/10 = 117.5

3. Geometric mean:

√100 * 135 = √13,500 = 116.2 (Rounding to the next tenth)

4. Harmonic mean:

2/(1/100 + 1/135) = 2/(0.01 + 0.0074) = 114.9 (Rounding to the next tenth)