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Arithmetic Progression 



Problem 18 of 19 


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










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Arithmetic Progression 
18. 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 `a3d, ad, a+d, a+3d`
Addition of last 2 term is `14`
`=> (a3d) + (a+3d) = 14`
`=> 2a = 14`
`=> a = 14/2 = 7`
Now multiplication of middle two terms is `45`
`=> (ad) (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 : `73(2), 72, 7+2, 7+3(2) => 1, 5, 9, 13`
`d = 2 =>` Required terms : `73(2), 7(2), 72, 73(2) => 13, 9, 5, 1`









