a.

The arithmetic sequence of odd natural numbers is .

The common difference is .

Find :

Find :

b.

Since the sum of the first odd natural numbers is and the sum of the first is , the sum

of the first terms of the sequence of odd natural numbers appears to be .

c.

Explicit formula for the arithmetic sequence of odd natural numbers :

.

Substitute and into the formula for the sum of a finite arithmetic series

a.

and .

b.

The sum of the first terms of the sequence of odd natural numbers appears to be

c.

The algebric proof is verified.