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Problem: 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 [ Calculator, Method and examples ]

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Your problem `->` 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 `a-3d, a-d, a+d, a+3d`

Addition of this terms is `4`

`=> (a-3d) + (a-d) + (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`

`=> (a-3d) (a+3d) + (a-d) (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 : `1-3(2), 1-2, 1+2, 1+3(2) => -5, -1, 3, 7`

`d = -2 =>` Required terms : `1-3(-2), 1-(-2), 1-2, 1-3(2) => 7, 3, -1, -5`






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