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Arithmetic Progression 



Problem 19 of 19 


19. For arithemetic progression, addition of four terms is and addition of multiplication of end terms and multiplication of middle terms is , then find that numbers










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Arithmetic Progression 
19. For arithemetic progression, addition of four terms is 4 and addition of multiplication of end terms and multiplication of middle terms is 38 , then find that numbers
Let the terms are `a3d, ad, a+d, a+3d`
Addition of this terms is `4`
`=> (a3d) + (ad) + (a+d) + (a+3d) = 4`
`=> 4 a = 4`
`=> a = 4/4 = 1`
Addition of multiplication of last 2 terms and middle 2 terms is `38`
`=> (a3d) (a+3d) + (ad) (a+d) = 38`
`=> (a^2  9d^2) + (a^2  d^2) = 38`
`=> 2a^2  10d^2 = 38`
`=> 2(1)^2  10d^2 = 38`
`=> 2  10d^2 = 38`
`=> 10d^2 = 40`
`=> d^2 = 4`
`=> d = + 2`
`d = +2 =>` Required terms : `13(2), 12, 1+2, 1+3(2) => 5, 1, 3, 7`
`d = 2 =>` Required terms : `13(2), 1(2), 12, 13(2) => 7, 3, 1, 5`





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