Question

Find the sum of all natural numbers between 602 and 902 which are not divisible by 4.

Answer 1

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

S_n = `"n"/2("a" + "l")`

S_n1 = `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

S_n2 = `75/2(604 + 900)`

= `75/2 xx 1504`

= 75 × 752

= 56400

Sum of the numbers which are not divisible by 4 = S_n1 – S_n2

= 224848 – 56400

= 168448

Sum of the numbers = 168448