Thursday, March 26, 2015

The arithmetic mean of three numbers is 23. The second number is six more than the first and the sum of the second and third terms is 54.Calculate...

Let the 1st term or number of the AP be x
.


The second number of the AP = x+6 by
data.


By another condtion, sum of the 1st 2nd and third
 numbers = 54.


 Threfore the 3rd number = 54 -(first
+second) = 54 -(x+x+6) = 54-2x-6 = 48-2x.


Since x ,  x+6
and 48-2x are inAP, they must have the equal  common increment  between any two
successive terms. Or


2nd term -1st term = 3rd term -2nd
term


x+6-x = 48-2x -(x+6)


6 =
42 -3x.


3x= 42-6 =36


3x/x =
36/3


x = 12.


So the three
numbers in AP are x, x+6 and x+12


 and they are  12,18, 24.
Obviously they satisfy the condtion. of their sum = 54 .

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