Find 4 numbers in AP such that their sum is 32 and the sum of their sq

1.	Find 4 numbers in AP such that their sum is 32 and the sum of their squares is 336
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=32{tex}\\therefore{/tex}4a = 32\xa0{tex}\\Rightarrow{/tex}\xa0a = 8Sum 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=336{tex}\\therefore{/tex}4(a2+5d2)=336{tex}\\Rightarrow{/tex}a2+5d2=84 [{tex}\\because {/tex}a=8]{tex}\\Rightarrow{/tex}5d2= 84-64{tex}\\Rightarrow{/tex}5d2=20{tex}\\Rightarrow{/tex}d2=4{tex}\\Rightarrow{/tex}d={tex} \\pm {/tex}2Hence, the required numbers (2, 6, 10, 14).

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