Question

Find the sum of all numbers from 1 to 200 which are divisible by either 2 or 3.

Answer 1

1. Sum of numbers divisible by 2:

The numbers divisible by 2 from 1 to 200 are: 2, 4, 6, ..., 200.

a = 2

l = 200

n = `200/2`

= 100

`S_2 = n/2 (a + l)`

`S_2 = 100/2 (2 + 200)`

= 50 × 202

= 10,100

2. Sum of numbers divisible by 3:

The numbers divisible by 3 from 1 to 200 are: 3, 6, 9, ..., 198.

a = 3

l = 198

n = `198/3`

= 66

`S_3 = n/2 (a + l)`

`S_3 = 66/2 (3 + 198)`

= 33 × 201

= 6,633

3. Sum of numbers divisible by both 2 and 3 (Divisible by 6)

The numbers divisible by 6 from 1 to 200 are: 6, 12, 18, ...,198

a = 6

l = 198

n = `198/6`

= 33

`S_6 = n/2 (a + l)`

`S_6 = 33/2 (6 + 198)`

= `33/2 × (204)`

= `33 xx 204/2`

= 33 × 102

= 3,366

Total = S₂ + S₃ − S₆

= 10,100 + 6,633 − 3,366

= 13,367