Question

the sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is_____
a) 10.200
(b) 30,000
(c)8200
(d)2200
​

Answer 1

Sum of first 'n' natural no =n(n+1)/2

sum of any numbers =n/2(1st number + last number)

now,

(300×301/2)-(100×101/2)=40100..gives sum of natural numbers between 100 and 300..

1-300.,75 numbers are div by 4

1-100.,25 numbers are div by 4

75/2(4+300)-25/2(4+100)=10100..this is sum of all numbers div by4 between 100 to 300

hence 40100-10100=30000 is required answer..

Answer 2

am doing this while keeping in mind that it is for objective paper

that's why i hve tried my best to skip as much steps as i can, but still i hv mentioned those identities which i hv used while processing the qstn