Question

) What is the sum of all natural numbers between 100 to 1000 which leaves
remainder 1 when divided by 4​

Answer 1

Answer:

98540 is the sum of all natural number

Answer 2

Step-by-step explanation:

1st term btween 100 and 1000 whicg remainder is 1 when divided by 4 is 101

#ultra pro max tip - when 100 / 4 is done remainder is 0 so just add 1 to obtain the number so its 101

the last term which remainder is 1 when divided by 4 is 997

#ultrapromax tip 2 - when 1000/4 remainder is 0 so just minus 4 from 1000 which will be 996 just use ultrapromax tip 1 so the number is 997

AP FORMED -

101 , 105 , 109........997. [ a = 101 , d = 4 ]

l = 997

997 = a + (n - 1)(d)

997 = 101 + (n - 1)(4)

997 - 101 = (n - 1)(4)

896 ÷ 4 = n - 1

n = 224 + 1 = 225

n = 225

sum of all 225 terms

s= n/2 [ 2a + ( n - 1 ) ( d ) ]

= 225 / 2 [ 2(101) + 224(4)]

= 225 [ 101 + 448 ]

= 225( 549 )

= 123525

123525 answer