Question

find the sum of first 100 odd natural numbers​

Answer 1

Answer:

sum of n terms formula is

Sn=n/2(a+an)

Step-by-step explanation:

n =100

since they are odd natural numbers

a=1

and d=3-1=2

an=a+(n-1)d

1+(100-1)(2)

1+(99)(2)

1+198

=199

S100=100/2(1+199)

=50(200)

10000

Answer 2

Given:

First 100 odd natural numbers.

To find:

The sum of the first 100 odd natural numbers.

Solution:

The sequence of the first 100 odd natural numbers is:

1, 3, 5, 7, till 100 odd natural numbers.

This forms an arithmetic progression (A.P.) in which the sum of terms 'S' is given by:

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

where 'd' is a common difference, 'a' is the first term, n = number of terms till nth term.

So,

in the sequence 1, 3, 5, 7, till 100 odd natural numbers,

a = 1, d = second term - first term = 3 - 1 = 2, n = 100

Now,

The sum of odd natural numbers is

$= \frac{100}{2} [2(1) + (100 - 1)2]$

$= 50 [2 + (99)2]$

$= 50 (2 + 198)$

$= 50 \times 200$

$= 10,000$

Hence, the sum of odd natural numbers is 10,000.