Find the sum of all natural numbers lying between 100 and 1000 which are multiples of 5.

The numbers lying between 100 and 1000 that are multiples of 5 are

105, 110, 115, 120,…, 995

a₂ – a₁ = 110 – 105 = 5

a₃ – a₂ = 115 – 110 = 5

∵ a₃ – a₂ = a₂ – a₁ = 5

Therefore, the series is in AP

Here, a = 105, d = 5 and a_n = 995

We know that,

a_n = a + (n – 1)d

⇒ 995 = 105 + (n – 1)5

⇒ 995 – 105 = (n – 1)5

⇒ 890 = (n – 1)5

⇒ 178 = (n – 1)

⇒ n = 179

Now, we have to find the sum of this AP

⇒ S₁₇₉ = 179[105 + 89 × 5]

⇒ S₁₇₉ = 179 [550]

⇒ S₁₇₉ = 98450

Hence, the sum of all numbers lying between 100 and 1000 that are multiples of 5 is 98450.