What is the Sum of the First 70 Odd Numbers?

The sum of the first 70 odd numbers is 4900.

Understanding the Sum of Odd Numbers

The sum of the first n odd numbers can be calculated using a simple formula:

S_n = n²

Where:

• S_n is the sum of the first n odd numbers
• n is the number of odd numbers

Calculation

In this case, we want to find the sum of the first 70 odd numbers. Therefore, n = 70. Applying the formula:

S₇₀ = 70² = 70 * 70 = 4900

Example

Let's illustrate this with a smaller example. What is the sum of the first 5 odd numbers?

1. The first 5 odd numbers are: 1, 3, 5, 7, 9
2. Their sum is: 1 + 3 + 5 + 7 + 9 = 25
3. Using the formula: S₅ = 5² = 25

This confirms the validity of the formula.

Conclusion

Therefore, the sum of the first 70 odd numbers is 4900. This is a straightforward application of the sum of odd numbers formula.