Question

How many numbers of three digits are divisible by 9?

Answer 1

To find the number of terms (n), use the formula for the nth term of an AP:

a_n = a₁ + (n − 1)d

Substitute the values a_n = 999, a₁ = 108, and d = 9:

999 = 108 + (n − 1)9

Subtract 108 from both sides.

999 − 108 = (n − 1)9

⇒ 891 = (n − 1)9

⇒ `891/9 = (n − 1)`

⇒ 99 = (n − 1)

⇒ 99 + 1 = n

⇒ 100 = n