Solve the equation –4 + (–1) + 2 + …. + x = 437.


Given equation is - 4 + (- 1) + 2 + - - - + x = 437


Its terms can be listed as


- 4, - 1, 2, - - - , x


And this is an AP with First term, a = - 4


Common difference, d = - 1 - (- 4) = 3


Let the no of terms be n


Then Sum of first n terms, Sn = 437



n[ 2 (- 4) + (n - 1)3] = 874


n (- 8 + 3n - 3) = 874


n(3n - 11) = 874


3n2 - 11n - 874 = 0


Solving this quadratic equation with


A = 3


B = - 11


C = - 874


Then D = b2 - 4ac = (- 11)2 - 4(3) (- 874)


= 121 + 10488 = 10609





(not possible as n is a natural no)


so x is the 19th term of AP


x = a19 = a + 18d


= - 4 + 18(3)


= 50


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