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

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

Solution :

Sum of all natural number between 602 and 902

  =  Sum of all number between 602 and 902 - Sum of numbers which are divisible by 4 between 602 and 902

Sum of all number between 602 and 902 :

  =  [603 + 604 +................ + 901] 

n = [(l - a)/d] + 1 n = [(901-603)/1]+1 n = 298 + 1 n  = 299

Sn  = (n/2)[a + l] S301  = (299/2)[603 + 901]   =  (299/2)[1504]   =  299(752)   =  224848

Sum of numbers which are divisible by 4 between 602 and 902.

  =  604 + 608 + 612 + .......... + 900

n  = [(l - a)/d] + 1

=  [(900 - 604)/4] + 1

n  = 75

Sn  = (n/2)[a + l]

S75  = (75/2)[604 + 900]

  =  (75/2)[1504]

  =  75(752)

  =  56400

Required sum  = 224848 - 56400

=  168448