Find the sum:$2 + 4 + 6 + ……….. + 200$

Given:

Given sequence is $2 + 4 + 6 + ……….. + 200$.

To do:

We have to find the sum of $2 + 4 + 6 + ……….. + 200$.

Solution:

Here,

\( 2+4+6+\ldots+200 \) is in A.P.

\( a=2, d,=4-2=2 \) and \( l=200 \)

We know that,

\( a_{n}=a+(n-1) d \)

\( \Rightarrow 200=2+(n-1) \times 2 \)
\( \Rightarrow 200=2+2 n-2 \)

\( \Rightarrow 2 n=200 \)

\( \Rightarrow n=100 \)
\( S_{n}=\frac{n}{2}[a+l] \)
\( =\frac{100}{2}[2+200] \)
\( =\frac{100}{2} \times 202=10100 \)

Therefore, the sum of the given sequence is 10100. 

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Updated on: 10-Oct-2022

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