Question
Find the sum of first n odd natural numbers.
✓
Answer
In this problem, we need to find the sum of first n odd natural numbers.
So, we know that the first odd natural number is $1$. Also, all the odd terms will form an A.P. with the common difference of $2$.
So here,
First term $(a) = 1$
Common difference $(d) = 2$
So, let us take the number of terms as n
Now, as we know,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
So, for n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2(1)+(\text{n}-1)2]$
$=\frac{\text{n}}{2}[2+2\text{n}-2]$
$=\frac{\text{n}}{2}(2\text{n})$
$=\text{n}^2$
Therefore, the sum of first n odd natural numbers is $S_n = n^2$.
So, we know that the first odd natural number is $1$. Also, all the odd terms will form an A.P. with the common difference of $2$.
So here,
First term $(a) = 1$
Common difference $(d) = 2$
So, let us take the number of terms as n
Now, as we know,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
So, for n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2(1)+(\text{n}-1)2]$
$=\frac{\text{n}}{2}[2+2\text{n}-2]$
$=\frac{\text{n}}{2}(2\text{n})$
$=\text{n}^2$
Therefore, the sum of first n odd natural numbers is $S_n = n^2$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In an A.P., the first term is $2$, the last term is $29$ and the sum of the terms is $155$. Find the common difference of the A.P.
→If PT is a tangent to a circle with centre O and PQ is a chord of the circle such that $\angle\text{QPT} = 70^\circ$ then find the measure of $\angle\text{POQ}.$ 
→A solid metallic sphere of diameter 28cm is melted and recast into a number of smaller cones, each of diameter 4cm and height 3cm. Find the number of cones so formed.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p(y) = 5y^2 - 7y + 1$, find the value of $\frac{1}{\alpha}+\frac{1}{\beta}$
→Solve the following simultaneous equations using Cramer’s rule.
4x + 3y – 4 = 0; 6x = 8 – 5y
4x + 3y – 4 = 0; 6x = 8 – 5y
Prove that $\sqrt{\frac{1+\cos A}{1}}=\operatorname{cosec} A+\cot A$
→The areas of two similar triangles are $81\ cm^2$ and $49\ cm^2$ respectively. Find the ratio of their corresponding heights. What is the ratio of their corresponding medians?
→Solve : x² + x + 5 = 0
A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:
- Red.
- Black or white.
- Not black.
Find the coordinates of the points which divide the line segment joining the points $(-2,2)$ and $(6,-6)$ in four equal parts.
→