find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

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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 *n*^{th} term of the AP.

*a _{n}* = 296

∴ 204 +(*n* – 1) × 4 = 296 ( *a _{n}*

_{ }=

*a*+ (

*n*– 1)

*d*)

⇒ 4(*n* – 1) = 296 – 204 = 92

⇒ *n* – 1 = 23

⇒ *n* = 24

Sum of all natural number between 200 and 800 which are divisible by 4

= 12 (408 + 23 × 4)

= 12 (408 + 92)

= 12 × 500

= 6000

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