Question

Find the sum of all the natural numbers less than 100 which are divisible by 6

Answer 1

Answer:

Hope it's helpful for you mate

please follow me

And please mark it as a brainlist

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Natural numbers less than 100 and divisible by 6:

6, 12, 18, 24, ... 96

This forms an AP with 'a' = 6 and 'd' = 6, 'aₙ' = 96

⇒ aₙ = a + ( n - 1 ) d

⇒ 96 = 6 + ( n - 1 ) 6

⇒ 96 - 6 = ( n -  1 ) 6

⇒ 90 = ( n - 1 ) 6

⇒ 90/6 = ( n - 1 )

⇒ 15 = n - 1

⇒ n = 15 + 1 = 16 terms

Sum of 'n' terms of an AP:

⇒ Sₙ = n/2 [ a + aₙ ]

⇒ S₁₆ = 16/2 [ 6 + 96 ]

⇒ S₁₆ = 8 ( 102 )

⇒ S₁₆ = 816

Therefore,

sum of all natural numbers less than 100 which are divisible by 6 is $\bold{816}$