If the sum of three consecutive terms of an A | vedclass

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Question

(a) Let consecutive terms of an $A.P.$ are $a - d,\;a,\;a + d$.

Under given condition, $(a - d) + a + (a + d) = 51$

$ \Rightarrow $ $a = 17$ and

Vedclass · Accepted Answer

$21, 17, 13$

Vedclass · Answer

(a) Let consecutive terms of an $A.P.$ are $a - d,\;a,\;a + d$.

Under given condition, $(a - d) + a + (a + d) = 51$

$ \Rightarrow $ $a = 17$ and $(a - d)(a + d) = 273$

$ \Rightarrow $ ${a^2} - {d^2} = 273$

$ \Rightarrow $ $ - {d^2} = 273 - 289$

$ \Rightarrow $ $d = 4$

Hence consecutive terms are $13, 17, 21.$

Trick : Both conditions are satisfied by $(a)$ $i.e.$ $21, 17, 13.$

If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of last and first term is $273$, then the numbers are

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