The sum of four numbers in A.P. is 50. The gr | vedclass

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(A) Let the four numbers in $A.P.$ be $(a-3d), (a-d), (a+d), (a+3d)$.Given that the sum is $50$:$(a-3d) + (a-d) + (a+d) + (a+3d) = 50$$4a = 50 \implie

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$5, 10, 15, 20$

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(A) Let the four numbers in $A.P.$ be $(a-3d), (a-d), (a+d), (a+3d)$.Given that the sum is $50$:$(a-3d) + (a-d) + (a+d) + (a+3d) = 50$$4a = 50 \implies a = 12.5$.The smallest number is $(a-3d)$ and the greatest number is $(a+3d)$.Given that the greatest number is four times the smallest:$(a+3d) = 4(a-3d)$$12.5 + 3d = 4(12.5 - 3d)$$12.5 + 3d = 50 - 12d$$15d = 37.5 \implies d = 2.5$.The numbers are:$12.5 - 3(2.5) = 12.5 - 7.5 = 5$$12.5 - 2.5 = 10$$12.5 + 2.5 = 15$$12.5 + 3(2.5) = 12.5 + 7.5 = 20$.Thus,the numbers are $5, 10, 15, 20$ or in reverse order $20, 15, 10, 5$.

The sum of four numbers in $A.P.$ is $50$. The greatest number is four times the smallest number. Find those numbers.

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