If the sum of three numbers of a arithmetic s | vedclass

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Question

(b) Let three numbers are $a - d,\;a,\;a + d$.

We get $a - d + a + a + d = 15$

$ \Rightarrow $$a = 5$

and ${(a - d)^2} + {a^2} + {(a + d)^2}

Vedclass · Accepted Answer

$3, 5, 7$

Vedclass · Answer

(b) Let three numbers are $a - d,\;a,\;a + d$.

We get $a - d + a + a + d = 15$

$ \Rightarrow $$a = 5$

and ${(a - d)^2} + {a^2} + {(a + d)^2} = 83$

$ \Rightarrow $ ${a^2} + {d^2} - 2ad + {a^2} + {a^2} + {d^2} + 2ad = 83$

$ \Rightarrow $$2({a^2} + {d^2}) + {a^2} = 83$

Putting $a = 5$

$ \Rightarrow $$2(25 + {d^2}) + 25 = 83$

$ \Rightarrow $$2{d^2} = 8$

$ \Rightarrow $$d = 2$

Thus numbers are $3, 5, 7.$

Trick : Since $3 + 5 + 7 = 15$

and ${3^2} + {5^2} + {7^2} = 83$.

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

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