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For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that numbers [ Calculator, Method and examples ]

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Your problem `->` For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that numbers


Let the terms are `a-d, a, a+d`

Addition of this terms is `51`

`=> (a-d) + a + (a+d) = 51`

`=> 3 a = 51`

`=> a = 51/3 = 17`

Multiplication of last 2 terms is `273`

`=> (a-d)(a+d) = 273`

`=> a^2 - d^2 = 273`

`=> d^2 = a^2 - 273`

`=> d^2 = (17)^2 - 273`

`=> d^2 = 289 - 273`

`=> d^2 = 16`

`=> d = +- 4`

`d = +4 =>` Required terms : `17 - 4, 17, 17 + 4 => 13, 17, 21`

`d = -4 =>` Required terms : `17-(-4), 17, 17-4 => 21, 17, 13`






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