Question

Sum of all the numbers of two digits?

Answer 1

Your answer is 4905.

Answer 2

Hey There,

Here, we are asked to find the sum of all two-digit numbers.

The two-digit numbers are 10,11,12, ... , 98, 99.

Here, we can easily see that it is an AP.

Here,

First Term = a = 10

Common Difference = d = 1

Let number of terms be n.


$T_n=a+(n-1)d \\ \\ \implies 99 = 10+(n-1)\times 1 \\ \\ \implies 99 = 10 + n - 1 \\ \\ \implies 99 = 9 + n \\ \\ \implies \boxed{n=90}$


Now, Sum of n terms of an AP is given as:


$S_n = \frac{n}{2} (\textrm{First Term + Last Term}) \\ \\ \\ \implies S=\frac{90}{2} (10+99) \\ \\ \\ \implies S = 45 \times 109 \\ \\ \\ \implies \boxed{S=4905}$


Thus, the Sum of all two-digit numbers = 4905



Hope it helps
Purva
Brainly Community