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For arithemetic progression of four terms, addition of end terms is 14 and multiplication of middle two terms is 45 , then find that numbers

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Your problem `->` For arithemetic progression of four terms, addition of end terms is 14 and multiplication of middle two terms is 45 , then find that numbers


Let the terms are `a-3d, a-d, a+d, a+3d`

Addition of last 2 term is `14`

`=> (a-3d) + (a+3d) = 14`

`=> 2a = 14`

`=> a = 14/2 = 7`

Now multiplication of middle two terms is `45`

`=> (a-d) (a+d) = 45`

`=> a^2 - d^2 = 45`

`=> d^2 = a^2 - 45`

`=> d^2 = 7^2 - 45`

`=> d^2 = 49 - 45`

`=> d^2 = 4`

`=> d = +- 2`

`d = +2 =>` Required terms : `7-3(2), 7-2, 7+2, 7+3(2) => 1, 5, 9, 13`

`d = -2 =>` Required terms : `7-3(-2), 7-(-2), 7-2, 7-3(2) => 13, 9, 5, 1`






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