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Arithmetic Progression 



Problem 17 of 19 


17. For arithemetic progression, addition of three terms is and multiplication of end terms is , then find that nos.










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Arithmetic Progression 
17. For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that nos.
Let the terms are `ad, a, a+d`
Addition of this terms is `51`
`=> (ad) + a + (a+d) = 51`
`=> 3 a = 51`
`=> a = 51/3 = 17`
Multiplication of last 2 terms is `273`
`=> (ad)(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, 174 => 21, 17, 13`







