Question

How to find the sum of all natural numbers from 100 to 300 which are not exactly divisible by 4 and 5

Answer 1

Answer:

Step-by-step explanation:

sum of numbers divisible by 4

= 100 + 104 + 108 + ... + 300

total numbers = 51

Sn = n/2[2a + (n – 1)d]

= 51/2[200 + 50 × 4]

= 51/2[400]

= 51 × 200

= 10200

sum of numbers divisible by 5

= 100 + 105 + 110 + 115 + ... + 300

total numbers = 41

Sn = n/2[2a + (n – 1)d]

= 41/2[200 + 40 × 5]

= 41/2[400]

= 41 × 200

= 8200

but above additions contain numbers which are divisible by 20 (LCM of 4 and 5)

to be subtracted.

sum of numbers divisible by 20

= 100 + 120, + 140, + ... + 300

total numbers = 11

= 11/2[200 + 10 × 20]

= 11 × 200

= 2200

required sum = 10200 + 8200 – 2200

= 16200