Class 11 Mathematics Sequence and Series: NCERT Solutions for Question 1

This page offers a step-by-step solution to the specific question NCERT Class 11th Mathematics - Sequence and Series | find the sum of odd integers from 1 to 2001 Answer from NCERT Class 11th Mathematics, Chapter Sequence and Series.
Question 1

Find the sum of odd integers from 1 to 2001.

Answer
The odd integers from 1 to 2001 are 1, 3, 5, …1999, 2001.
 
This sequence forms an A.P.
 
Here, first term, a = 1
 
Common difference, d = 2
 
Here,
 
\begin{align} a + (n - 1)d = 2001 \end{align}
 
\begin{align} => 1 + (n - 1)(2) = 2001 \end{align}
 
\begin{align} => 2n -2 = 2000 \end{align}
 
\begin{align} => n = 1001 \end{align}
 
\begin{align} S_n = \frac {n}{2}\left[2a + (n -1)d\right]\end{align}
 
\begin{align} \therefore S_n = \frac {1001}{2}\left[2 × 1 + (1001 -1)×2\right]\end{align}
 
\begin{align} = \frac {1001}{2}\left[2 + 1000×2\right]\end{align}
 
\begin{align} = \frac {1001}{2} × 2002\end{align}
 
\begin{align} =1001 × 1001 \end{align}
 
\begin{align} = 1002001 \end{align}
 
Thus, the sum of odd numbers from 1 to 2001 is 1002001.
 

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