Find four no. In AP whose sum is 28 and sum of square is 216 ? With so

1.	Find four no. In AP whose sum is 28 and sum of square is 216 ? With solution
Answer» Let the required number be (a - 3d), (a - d), (a + d) and (a + 3d)Sum of these numbers = (a - 3d) + (a - d)+ (a + d) + (a + 3d)According to the question, sum of the numbers=28{tex}\\therefore{/tex}4a = 28\xa0{tex}\\Rightarrow{/tex}\xa0a = 7Sum of the squares of these numbers=(a-3d)2+(a-d)2+(a+d)2+(a+3d)2=4(a2+5d{tex}^2{/tex})Now, sum of the squares of numbers=216{tex}\\therefore{/tex}4(a2+5d2)=216{tex}\\Rightarrow{/tex}a2+5d2=54 [{tex}\\because {/tex}a=7]{tex}\\Rightarrow{/tex}5d2= 54-49{tex}\\Rightarrow{/tex}5d2=5{tex}\\Rightarrow{/tex}d2=1{tex}\\Rightarrow{/tex}d={tex} \\pm {/tex}1Hence, the required numbers (4, 6, 8, 10).

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