n(n + 1) = 420 …Given{tex}\\Rightarrow n ^ { 2 } + n = 420{/tex}{tex}\\Rightarrow n ^ { 2 } + n – 420 = 0{/tex}Comparing with An2 + Bn + C = 0, we getA = 1, B = 1, C = -420Using the quadratic formula, {tex}n = \\frac { – B \\pm \\sqrt { B ^ { 2 } – 4 A C } } { 2 A }{/tex}we get {tex}\\Rightarrow \\frac { – 1 \\pm \\sqrt { 1 + 1680 } } { 2 } = \\frac { – 1 \\pm \\sqrt { 1681 } } { 2 }{/tex}{tex}= \\frac { – 1 \\pm 41 } { 2 } = \\frac { – 1 + 41 } { 2 } , \\frac { – 1 – 41 } { 2 } = 20 , – 21{/tex}n = -21 is in admissible as n is the number of terms.{tex}\\therefore n = 20{/tex}Hence, the required value of n is 20.