Question

Sum of all natural numbers between 602 and 902 which are not divisible by 4

Answer 1

Answer:

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