Find 4 number in Ap whose some is 20 and the some of whose square is 1

1.	Find 4 number in Ap whose some is 20 and the some of whose square is 120
Answer» Let the required numbers in A.P. are (a - 3d), (a - d), (a + d) and (a + 3d).ATQ,(a -3d) + (a - d) + (a + d) + (a + 3d) = 20 [given, Sum = 20]{tex}\\Rightarrow{/tex}\xa04a = 20{tex}\\Rightarrow{/tex}\xa0a = 5.Also A.T.Q:-\xa0(a - 3d)2 + (a - d)2 + (a + d)2\xa0+ (a + 3d)2 = 120{tex}\\Rightarrow{/tex}4(a2 + 5d2) = 120{tex}\\Rightarrow{/tex}(a2 + 5d2) = 30{tex}\\Rightarrow{/tex}\xa025 + 5d2 = 30. [Since,\xa0a =\xa05]{tex}\\Rightarrow{/tex}\xa05d2 = 5\xa0{tex}\\Rightarrow{/tex}\xa0d2 = 1\xa0{tex}\\Rightarrow{/tex}\xa0d = {tex} \\pm {/tex}\xa01.Thus, a = 5 and d = {tex} \\pm {/tex}1.When a = 5 & d = 1The required numbers are (2,4,6,8)\xa0When a = 5 & d = -1The required numbers are (8, 6,4,2)

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