Question

Find the sum of
first n
odd numbers.​

Answer 1

Answer:

the sum of first n odd number

Step-by-step explanation:

Let, the odd number =n

Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\orange{\underline{\underline{To \ find}}}$

Sum of first n odd numbers.

$\bold\green{\underline{\underline{Solution}}}$

Odd numbers are

1,3, 5,7,.....,n

In the above serie

Let t1 be 1, t2 be 3, t3 be 5 and t4 be 7

t2-t1=3-1=2

t3-t2=5-3=2

t4-t3=7-5=2

Therefore common difference is 2 and above sequence is an A.P.

Sum of first n odd numbers is

$\bold{Sn=\frac{n}{2}[2a+(n-1)d]}$

$\bold{Sn=\frac{n}{2}[2(1)+(n-1)×2]}$

$\bold{Sn=\frac{n}{2}[2+2(n-1)]}$

Therefore sum of first n natural numbers is

$\bold{\frac{n}{2}[2+2(n-1)]}$.