find four numbers in A.P whose sum is 20 and the sum of whose squares is 180.

Let the four numbers in A.P. be .

Given, 

Given, 

When a = 5 and d = 2, we get

When a = 5 and d = –2, we get

Thus, four numbers in A.P. are –1, 3, 7 and 11.


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