Find the sum of the numbers lying between 107 and 253 that are multiples of 5.

The numbers lying between 107 and 253 that are multiples of 5 are

110, 115, 120,…, 250

a₂ – a₁ = 115 – 110 = 5

a₃ – a₂ = 120 – 115 = 5

∵ a₃ – a₂ = a₂ – a₁ = 5

Therefore, the series is in AP

Here, a = 110, d = 5 and a_n = 250

We know that,

a_n = a + (n – 1)d

⇒ 250 = 110 + (n – 1)5

⇒ 250 – 110 = (n – 1)5

⇒ 140 = (n – 1)5

⇒ 28 = (n – 1)

⇒ n = 29

Now, we have to find the sum of this AP

⇒ S₂₉ = 29[110 + 14 × 5]

⇒ S₂₉ = 29[180]

⇒ S₂₉ = 5220

Hence, the sum of all numbers lying between 107 and 253 is 5220.