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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 ]Solution: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 numbersLet the terms are a-3d, a-d, a+d, a+3dAddition of this terms is 4=> (a-3d) + (a-d) + (a+d) + (a+3d) = 4=> 4 a = 4=> a = 4/4 = 1Addition 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 = +- 2d = +2 => Required terms : 1-3(2), 1-2, 1+2, 1+3(2) => -5, -1, 3, 7d = -2 => Required terms : 1-3(-2), 1-(-2), 1-2, 1-3(2) => 7, 3, -1, -5

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