Find the sum of odd integers from 1 to 2001. - Vidyadip

Question

Find the sum of odd integers from 1 to 2001.

✓

Answer

Odd integers from 1 to 2001 are $1,3,5,7, \ldots, 2001$.
Here, $a=1, d=3-1=2$ and $a_n=2001$
$\therefore a_n=a+(n-1) d$
$\therefore 2001=1+(n-1) \times 2$
$\Rightarrow 2001-1=(n-1) \times 2$
$\Rightarrow \frac{2000}{2}=(n-1)$
$\Rightarrow n=1000+1=1001$
Now, $\mathrm{S}_{\mathrm{n}}=\frac{n}{2}(\mathrm{a}+\mathrm{I})$
$\Rightarrow S_{1001}=\frac{1001}{2}(1+2001)$
$\Rightarrow S_{1001}=\frac{1001}{2} \times 2002=1002001$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from SEQUENCES AND SERIES→SEQUENCES AND SERIES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100 m$ long is supported by vertical wires attached to the cable, the longest wire being $30 m$ and the shortest being $6 m$. Find the length of a supporting wire attached to the roadway $18 m$ from the middle.

If $a, b, c$ and $d$ are in G.P show that $\left(a^2+b^2+c^2\right)\left(b^2+c^2+d^2\right)=(a b+b c+c d)^2$.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that: $(\text{A}\cup\text{B})'=\text{A'}\cap\text{B'}$

Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x - y = 0

Prove that:$\frac{\cos8^\circ-\sin8^\circ}{\cos8^\circ+\sin8^\circ}=\tan37^\circ$$ $

Differentiate the following function with respect to x:$(\text{2x}^2-3)\sin\text{x}$

Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Find a G.P. for which sum of the first two terms is -4 and the fifth term is 4 times the third term.

Sketch the graphs of the following function: $\text{u(x)}=\sin^2\text{x},0\leq\text{x}\leq2\pi$ $\text{v(x)}=|\sin\text{x}|,0\leq\text{x}\leq2\pi$