The sum of the first twenty even natural numb | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(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 $\ldots \ldots \ldots \ldots$

Similar Questions

For the $A.P.$ formed by positive multiples of $4$,$d = \ldots \ldots \ldots \ldots .$

For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$

In an $AP$,if $a = 1$,$a_{n} = 20$,and $S_{n} = 399$,then $n$ is:

For an $A.P.$,the first term is $5$ and the common difference is $3$. Then,the $15^{th}$ term of the $A.P.$ is..........

Solve the equation: $1+4+7+10+\ldots+x=287$

Vedclass Test Series

Exam Paper Generator

Online Exam Module