To find the sum of the first 30 odd numbers, we can use a known mathematical property about odd numbers.
### Step-by-Step Solution:
1. Understanding the Pattern:
The first few odd numbers are:
[tex]\(1, 3, 5, 7, 9, \ldots\)[/tex]
2. Pattern Recognition:
A useful property to know is that the sum of the first [tex]\(n\)[/tex] odd numbers is equal to [tex]\(n^2\)[/tex]. For example:
- The sum of the first 1 odd number (1) is [tex]\(1^2 = 1\)[/tex].
- The sum of the first 2 odd numbers (1 + 3) is [tex]\(2^2 = 4\)[/tex].
- The sum of the first 3 odd numbers (1 + 3 + 5) is [tex]\(3^2 = 9\)[/tex].
3. Application:
Based on this property, the sum of the first 30 odd numbers can be found by squaring 30.
4. Calculation:
[tex]\[
30^2 = 900
\][/tex]
Therefore, the sum of the first 30 odd numbers is [tex]\(\boxed{900}\)[/tex].
