To find the sum of the first 29 natural numbers ([tex]\(1 + 2 + 3 + \ldots + 29\)[/tex]), we use the formula for the sum of the first [tex]\( n \)[/tex] natural numbers. The sum [tex]\( S \)[/tex] of the first [tex]\( n \)[/tex] natural numbers is given by:
[tex]\[ S = \frac{n(n + 1)}{2} \][/tex]
Here, [tex]\( n \)[/tex] is 29.
1. Substitute [tex]\( n = 29 \)[/tex] into the formula:
[tex]\[ S = \frac{29(29 + 1)}{2} \][/tex]
[tex]\[ S = \frac{29 \times 30}{2} \][/tex]
2. Calculate the product inside the numerator:
[tex]\[ 29 \times 30 = 870 \][/tex]
3. Divide by 2:
[tex]\[ S = \frac{870}{2} = 435 \][/tex]
Thus, the sum of the numbers from 1 to 29 is 435.
The correct answer is:
D. 435
