Question

Find the sum of all two digit natural numbers which are divisible by 9.​

Answer 1

The sum of all the two digit natural numbers which are divisible by 9 is 585.

Step-by-step explanation:

Method 1. Using A.P.

The two digit natural numbers which are divisible by 9 are

18, 27, 36, ... ..., 90, 99

Here, the first number is 18 and the last number is 99.

Let, 99 be the n-th number.

Then, 18 + (n - 1) × 9 = 99

⇒ 18 + 9n - 9 = 99

⇒ 9n = 90

⇒ n = 10

So, there are 10 terms in the above sequence.

Thus the sum of terms in the sequence is

S = $\dfrac{n}{2}$ (first term + last term)

= $\dfrac{10}{2}$ (18 + 99)

= 5 × 117

= 585

Method 2. Simple addition

The two digit natural numbers which are divisible by 9 are

18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Thus their sum

= 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 + 90 + 99

= 585

#SPJ3