If the sum of three numbers of an arithmetic | vedclass

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(B) Let the three numbers in the arithmetic sequence be $(a - d)$,$a$,and $(a + d)$.According to the problem,the sum of these numbers is $15$:$(a - d)

Vedclass · Accepted Answer

$3, 5, 7$

Vedclass · Answer

(B) Let the three numbers in the arithmetic sequence be $(a - d)$,$a$,and $(a + d)$.According to the problem,the sum of these numbers is $15$:$(a - d) + a + (a + d) = 15$$3a = 15$$a = 5$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$Substituting $a = 5$ 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 $7, 5, 3$.In both cases,the set of numbers is ${3, 5, 7}$.

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

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