Find how many three digit natural numbers are divisible by 5.

1.	Find how many three digit natural numbers are divisible by 5.
Answer» The three digit natural numbers divisible by 5 are 100, 105, 110, …,995 The above sequence is an A.P. ∴ a = 100, d = 105 – 100 = 5 Let the number of terms in the A.P. be n. Then, t_n = 995 Since, t_n = a + (n – 1)d ∴ 995 = 100 +(n – 1)5 ∴ 995 – 100 = (n – 1)5 ∴ 895 = (n – 1)5 ∴ n – 1 = 895/5 ∴ n – 1 = 179 ∴ n = 179 + 1 = 180 ∴ There are 180 three digit natural numbers which are divisible by 5.

Answer»

The three digit natural numbers divisible by

5 are 100, 105, 110, …,995

The above sequence is an A.P.

∴ a = 100, d = 105 – 100 = 5

Let the number of terms in the A.P. be n. Then, t_n = 995

Since, t_n = a + (n – 1)d

∴ 995 = 100 +(n – 1)5

∴ 995 – 100 = (n – 1)5

∴ 895 = (n – 1)5

∴ n – 1 = 895/5

∴ n – 1 = 179

∴ n = 179 + 1 = 180

∴ There are 180 three digit natural numbers which are divisible by 5.

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