If the sum of three numbers in an arithmetic | vedclass

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(B) Let the three numbers be $a - d, a, a + d$.Given the sum of the numbers is $15$:$(a - d) + a + (a + d) = 15$$3a = 15$$a = 5$Given the sum of their

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$3, 5, 7$

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(B) Let the three numbers be $a - d, a, a + d$.Given the sum of the numbers is $15$:$(a - d) + a + (a + d) = 15$$3a = 15$$a = 5$Given the sum of their squares is $83$:$(a - d)^2 + a^2 + (a + d)^2 = 83$$(a^2 - 2ad + d^2) + a^2 + (a^2 + 2ad + d^2) = 83$$3a^2 + 2d^2 = 83$Substitute $a = 5$ into the equation:$3(5^2) + 2d^2 = 83$$3(25) + 2d^2 = 83$$75 + 2d^2 = 83$$2d^2 = 8$$d^2 = 4$$d = \pm 2$If $d = 2$,the numbers are $5-2, 5, 5+2$,which are $3, 5, 7$.If $d = -2$,the numbers are $5-(-2), 5, 5+(-2)$,which are $7, 5, 3$.Thus,the numbers are $3, 5, 7$.

If the sum of three numbers in an arithmetic sequence is $15$ and the sum of their squares is $83$,then the numbers are

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