The sum of the first twenty even natural numb | vedclass

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(B) The sequence of even natural numbers forms an Arithmetic Progression ($A$.$P$.) given by $2, 4, 6, 8, \ldots$Here,the first term $a = 2$,the commo

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$420$

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(B) The sequence of even natural numbers forms an Arithmetic Progression ($A$.$P$.) given by $2, 4, 6, 8, \ldots$Here,the first term $a = 2$,the common difference $d = 4 - 2 = 2$,and the number of terms $n = 20$.The sum of the first $n$ terms of an $A$.$P$. is given by the formula: $S_n = \frac{n}{2} [2a + (n - 1)d]$.Substituting the values: $S_{20} = \frac{20}{2} [2(2) + (20 - 1)2]$.$S_{20} = 10 [4 + (19 	imes 2)]$.$S_{20} = 10 [4 + 38]$.$S_{20} = 10 	imes 42 = 420$.Alternatively,the sum of the first $n$ even natural numbers is given by $n(n + 1)$.For $n = 20$,sum $= 20 	imes (20 + 1) = 20 	imes 21 = 420$.

The sum of the first twenty even natural numbers is $\ldots \ldots \ldots \ldots$

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