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Question
How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?
Solution
The natural numbers between 1 and 1000, which are divisible by 5 but not by 2, are:
5, 15, 25, 35, .......... 995
The above sequence is an A.P. with a common difference of 10.
Using formula, l = a + (n – 1)d
995 = 5 + (n – 1)10
⇒ `990/10` = n – 1
⇒ n – 1 = 99
⇒ n = 100
Thus, there are 100 terms between 1 and 1000, which are divisible by 5 but not by 2.
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