Question

What is the sum of all two digit even natural numbe

Answer 1

The sum of two digit even natural number is always even natural number

Answer 2

Answer:

2430 is the sum of all two digit even natural number.

Step-by-step explanation:

Explanation:

As we know that, there are total 45 two digit even numbers.

These are , 10, 12 ,14 ,16 .......98.

And the formula of sum of n term of A.P =$\frac{n}{2} [2a + (n - 1)d]$.

Step 1:

So , from the question we have ,

 10, 12 ,14 ,16 .......98.

Therefore, a = 10 , d = 12 - 10 = 2  and n = 45.

Now, from the formula,

$S_n$ = $\frac{n}{2} [2a + (n-1)d]$

$S_{45}$ = $\frac{45}{2}$[2(10)+(45 - 1)2]

$S_{45}$ = $\frac{45}{2}$[20 +44 × 2]

$S_{45}$ = $\frac{45}{2}$[20 + 88]

$S_{45}$ = $\frac{45}{2}$ ×108= 45×54 = 2430.

Final answer:

Hence, the sum of all two digit even natural number is 2430.

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