Question

The sum of all two digit numbers is ______.

Options

• 9810

• 9045

• 4509

• 4905

Answer 1

The sum of all two digit numbers is 4905.

Explanation:

The two digit numbers are 10, 11, 12, 13, ......, 99

Which forms A.P with first term = a = 11

And d = common difference = 12 – 11 = 1

And l = 99

We know that,

l = T_n

`\implies` 99 = a + (n – 1)d

`\implies` 99 = 10 + (n – 1)

`\implies` 99 = 9 + n

`\implies` n = 90

Since `S_n = n/2[a + l]`

`\implies S_90 = 90/2[10 + 99]`

`\implies` S₉₀ = 45 × 109 

`\implies` S₉₀ = 4905