Answer :

We know that the sum of 3 numbers in the AP is 18.


Let’s say that those 3 numbers are: a – d, a, a + d


So we can say that, a – d + a + a + d = 18


3a = 18


a= 6


Now, we have that the sum of squares of these 3 numbers is 180.


So we can say that, (a – d) 2 + a2 + (a + d) 2 = 180


a2 – 2ad + d2 + a2 + a2 + 2ad + d2 = 180


3a2 + 2d2 = 180


We know that a = 6,


So, 3(6)2 + 2d2 = 180


3(36) + 2d2 = 180


108 + 2d2 = 180


2d2 = 180 – 108


2d2 = 72


d2 = 36


d = 6


Now, our 3 numbers a – d, a, a + d are 6 – 6, 6, 6 + 6 = 0, 6, 12 respectively.


The 3 numbers of the A.P in the increasing order are : 0, 6, 12.


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