Find the four arithmetic means between 100 and 135. Show work.
2 answers:
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 = 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
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