Question

Show that the nth odd natural number is 2n
$- 1$

Answer 1

Odd numbers are 1 , 3 , 5 , 7 .... n Odd numbers forms an AP ( arithmetic progression ) where
a = first term = 1 and d = common difference = 3 - 1 = 2

nth term
= general term of an Ap
= a + ( n - 1 ) d
= 1 + ( n - 1 ) (2)
= 1 + 2n - 2
= 2n - 1