4 + (-1) +2+.....+x =437

1.	4 + (-1) +2+.....+x =437
Answer» (-4) + (-1) + 2 + 5 + ---- + x = 437.Now,-1 - (-4) = -1 + 4 = 32 - (-1) = 2 +\xa01 = 35 - 2 = 3Thus, this forms an A.P. with a = -4, d = 3,l = xLet their be n terms in this A.P.Then,Sn\xa0=\xa0{tex}\\frac { n } { 2 } [ 2 a + ( n - 1 ) d ] {/tex}{tex}\\Rightarrow 437 = \\frac { n } { 2 } [ 2 \\times ( - 4 ) + ( n - 1 ) \\times 3 ]{/tex}{tex}\\Rightarrow{/tex}\xa0874 = n[-8 + 3n - 3]{tex}\\Rightarrow{/tex}874 = n[3n - 11]{tex}\\Rightarrow{/tex}874 = 3n2\xa0- 11n{tex}\\Rightarrow{/tex}3n2\xa0- 11n - 874 = 0{tex}\\Rightarrow{/tex}3n2\xa0- 57n + 46n - 874 = 0{tex}\\Rightarrow{/tex}3n(n - 19) + 46(n - 19) = 0{tex}\\Rightarrow{/tex}3n + 46 = 0 or n = 19{tex}\\Rightarrow n = - \\frac { 46 } { 3 }{/tex}\xa0or n\xa0= 19Numbers of terms cannot be negative or fraction.{tex}\\Rightarrow{/tex}\xa0n = 19Now, Sn\xa0=\xa0{tex}\\frac { n } { 2 } [ a + l ]{/tex}{tex}\\Rightarrow 437 = \\frac { 19 } { 2 } [ - 4 + x ]{/tex}{tex}\\Rightarrow - 4 + x = \\frac { 437 \\times 2 } { 19 }{/tex}{tex}\\Rightarrow - 4 + x = 46{/tex}{tex}\\Rightarrow x = 50{/tex}

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