Find the sum:$1 + 3 + 5 + 7 + …….. + 199$

Given:

Given sequence is $1 + 3 + 5 + 7 + …….. + 199$.

To do:

We have to find the sum of $1 + 3 + 5 + 7 + …….. + 199$.

Solution:

Here,

\( 1+3+5+7+\ldots+199 \) is in A.P.

\( a=1, d=3-1=2 \) and \( l=199 \)

We know that,

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

\( \Rightarrow 199=1+(n-1) \times 2 \)
\( \Rightarrow 199=1+2 n-2 \)

\( \Rightarrow 2 n=199-1+2=200 \)
\( n=\frac{200}{2}=100 \)
\( S_{n}=\frac{n}{2}[a+l]=\frac{100}{2}(1+199) \)
\( =\frac{100}{2} \times 200=10000 \)

Therefore, the sum of the given sequence is $10000$. 

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Updated on: 10-Oct-2022

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