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
You might be interested in
The given three numbers are 5,8,24.
We have to use four operations (Adding, Subtracting,multiplication, division, square, square root, cube, cube root) out of these operation to make the result an irrational number.
There are many more examples that you can write.
Keep in mind
1. Sum of Rational and irrational is always irrational.
2. Difference of rational and irrational is always irrational.
As none of the 5,8,24 is a perfect square , nor addition of any two results in a perfect square, so square root of their addition or subtraction or multiplication results in an irrational number.
Similarly ,apart from 8, none of 5,24 is a perfect cube.So if you add or subtract any number from 8 and take their cube root or square root ,results in an irrational number.