Question

find the sum of all natural numbers less than 100 which are not divisible by 3? (answer : -3267)​

Answer 1

Answer:

4950 - 1683 = 3267

Step-by-step explanation:

sum of all natural numbers less than 100

AP is 1, 2, 3, 4 ...... 99

a = 1 d = 1

an = a + (n-1)d

99 = 1 + (n-1)1

99 = 1 + n - 1

n = 99

Sn = n/2 (2a + (n-1)d)

S99 = 99/2 (2(1) + (99-1)1)

= 99/2 ( 2 + 98)

= 99/2 × 100

= 99 × 50

= 4950. (1)

multiple of 3 less than 100

last number multiple of 3 less than 100 is 99

the AP is 3, 6, 9........99

a = 3 d = 3

99 = a + (n-1)d

99 = 3 + (n-1)3

99 = 3 + 3n - 3

99 = 3n

n = 99/3

n = 33

S33 = 33/2 ( 2(3) + (33-1)3)

= 33/2 (6 + 32(3))

= 33/2 (6 + 96)

= 33/2 × 102

= 33 × 51

= 1683 (2)

(1) - (2)

4950 - 1683 = 3267

hope you get your answer