The arithmetic mean (average) of two numbers c and d is given by overline{x} = frac{c+d}{2} The value overline{x} is equidistant between c and d, so t

sjeikdom0 2020-10-31 Answered
The arithmetic mean (average) of two numbers c and d is given by x=c+d2
The value x is equidistant between c and d, so the sequence c,x, d is an arithmetic sequence. inserting k equally spaced values between c and d, yields the arithmetic sequence c,X1,X2,X3,X4,...,Xk,d. Use this information for Exercise.
Insert four arithmetic means between 19 and 64.
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Expert Answer

Latisha Oneil
Answered 2020-11-01 Author has 100 answers
Step 1
Let the fourth arithmetic means between 19 and 64 are X1,X2,X3,X4
therefore,19,X1,X2,X3,X4,64 are in A.P with first term 19 and sixth term 64
a=19,a6=64
We know that first term of A.P is an=a+(n1)d
a6=a+(61)d
a6=a+5d
64=19+5d
5d=6419
5d=45
d9
Step 2
Now the arithmetic means can be calculated as follows
X1=a+d=19+9=28
X2=a+2d=19+2×9=37
X3=a+3d=19+3×5=46
X4=a+3d=19+4×5=55
Step 3
Ans: X1=28
X2=37
X3=46
X4=55
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