Sure! Let's solve the problem step-by-step.
We are given the arithmetic series:
[tex]\[ S = 1 + 2 + 3 + \ldots + 20 \][/tex]
To find the sum of the first [tex]\( n \)[/tex] natural numbers, we can use the formula for the sum of an arithmetic series:
[tex]\[ S = \frac{n(n + 1)}{2} \][/tex]
Here, [tex]\( n \)[/tex] is the last number in the series, which is 20.
Plug [tex]\( n = 20 \)[/tex] into the formula:
[tex]\[ S = \frac{20(20 + 1)}{2} \][/tex]
Let's simplify it step-by-step:
1. Calculate [tex]\( 20 + 1 \)[/tex]:
[tex]\[ 20 + 1 = 21 \][/tex]
2. Multiply the result by 20:
[tex]\[ 20 \times 21 = 420 \][/tex]
3. Divide by 2:
[tex]\[ \frac{420}{2} = 210 \][/tex]
So, the sum of the first 20 natural numbers is:
[tex]\[ S = 210 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{210} \][/tex]
Therefore, the answer is D. 210.
