Question

how many three digit terms are divisible by 6?

Answer 1

Dear Student,

The first three digit number divisible by 6 = 102.
Another three digit after 102 is 108.
​​​​​​Last three digit number divided by 6 = 999-3=996

So, AP is 102,108,....996

Here a=102, d=108-102=6
n=?

Now, as we know that,

l = a + (n – 1)d
⇒996=102+(n-1)6
⇒996=102+6n-6
⇒996=96+6n
⇒996-96=6n
⇒900=6n
⇒n= 900/6
⇒n=150
Therefore, there are 150 three digit numbers that are divisible by 6.

Regards