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

Question

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

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Answer

List of three digit number divisible by 5 are
100, 105,110,115,……….. 995
Let us find how many such number are there?
From the above sequence, we know that
t_n = 995, a = 100
t₁ = 105, t₂ = 110
Thus, d = t₂ – t₁ = 110 – 105 = 5
Now, By using n^th term of an A.P. formula
t_n = a + (n – 1)d
we can find value of “n”
Thus, on substituting all the value in formula we get,
995 = 100 + (n – 1)× 5
⇒ 995 – 100 = (n – 1)× 5
⇒ 895 = (n – 1) × 5
$\Rightarrow n -1=\frac{895}{5}=179$
⇒ n = 179 + 1 = 180

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