Question

show that the nth odd natural number is 2n-1

Answer 1

yes nth odd natural number is 2n-1
if a number is multiplied by 2 ,it would be even
so 2n is even
one less than even is odd
so 2n-1 is odd

Answer 2

Answer:

$n^{th}\:odd\: natural\:number = 2n-1$

Step-by-step explanation:

1,3,5,7,...,n are n odd natural numbers are in A.P.

$First \:term (a) = 1,\\common \: difference (d)=a_{2}-a_{1}\\=3-1\\=2$

$n^{th}\: term=a_{n}=a+(n-1)d$

$a_{n}=1+(n-1)2\\=1+2n-2\\=2n-1$

Therefore,

$n^{th}\:odd\: natural\:number = 2n-1$

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