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Question

Find the sum of the natural numbers between 200 and 300 divisible by 4

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Solution

The number between 200 and 300 which are divisible by 4 are 204, 208,.........,296.
204, 208,.........,296 are in AP.
Here a = 204 and d = 4
Let 296 be the nth term of the AP.
an = 296
∴ 204 +(n – 1) × 4 = 296
​​​​​​ (an = a + (n – 1)d)
⇒ 4(n – 1) = 296 – 204 = 92
⇒ n – 1 = 23
⇒ n = 24
Sum of all natural number between 200 and 300 which are divisible by 4
= 12 (408 + 23 × 4)
= 12 (408 + 92)
= 12 × 500
= 6000

Hope this helps :)

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