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Question
Find the sum of all natural numbers between 602 and 902 which are not divisible by 4.
Solution
First find the sum of all the natural’s number between 602 and 902
Here a = 603, d = 1, l = 901
n = `("l" - "a")/"d" + 1`
= `(901 - 603)/1 + 1`
= 298 + 1 = 299
Sn = `"n"/2("a" + "l")`
Sn1 = `299/2(603 + 901)`
= `299/2 xx 1504`
= 299 × 752
= 224848
Find the sum of all the numbers between 602 and 902 which are divisible by 4.
Here a = 604; l = 900; d = 4
n = `("l" - "a")/"d" + 1`
= `(900 - 604)/4 + 1`
= `296/4 + 1`
= 75
Sn2 = `75/2(604 + 900)`
= `75/2 xx 1504`
= 75 × 752
= 56400
Sum of the numbers which are not divisible by 4 = Sn1 – Sn2
= 224848 – 56400
= 168448
Sum of the numbers = 168448
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