Question

2. Find the number of natural numbers between 205 and 995 which are divisible by 2 and 5​

Answer 1

The total number of natural numbers, which are divisible by 2 and 5​ = 79

Step-by-step explanation:

The natural numbers between 205 and 995 which are divisible by 2 and 5​

(divisibe by 10) are:

210, 220, 230, ...., 990

The given sequence are in AP.

Here, first term (a) = 210, common difference (d) = 220 - 210 = 10 and

$a_{n}$ = 990

To find, the total number of natural numbers (n) = ?

We know that,

The nth term of an AP.

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

⇒ $210+(n-1)10=990$

⇒ (n - 1)10 = 990 - 210

⇒ (n - 1)10 = 780

⇒ n - 1 = 78

⇒ n = 78 + 1 = 79

Thus, the total number of natural numbers, which are divisible by 2 and 5​ = 79

Answer 2

The number of natural numbers between 205 and 995 which are divisible by 2 and 5 =79

Step-by-step explanation:

L.C.M of 5 and 2 = 10

The number of natural numbers between 205 and 995 which are divisible by 2 and 5 = (995÷10)-(205÷10)

                                  =99.5-20.5

                                   =79