Question

The number of three-digit odd positive integers is - (a) 450 (b) 500 (c) 550 (d) 600

Answer 1

101,........,999
by A.p
999=101+(n-1)2
999-101=n-1*2
898/2=n-1
449+1
450

Answer 2

The total number of three-digit odd positive integers = 450

Step-by-step explanation:

The number of three-digit odd positive integers are:

101, 103, 105, ...., 999

The given series are in AP.

To find, the total number of three-digit odd positive integers = ?

Here, first term (a) = 101, common difference(d) = 103 - 101 = 2 and

last tem$(a_{n})$ = 999

Let the number of term = n

We know that,

The nth term of an AP

$a_{n}=a+(n-1)d$

⇒ $101+(n-1)2=999$

⇒ $(n-1)2=999-101$

⇒ $(n-1)2=898$

⇒ $n-1=\dfrac{898}{2} =449$

⇒ n = 449 + 1 = 450

Hence, the total number of three-digit odd positive integers = 450