What is the sum of the first 95 odd natural numbers?

The sum of the first n odd natural numbers — 1, 3, 5, ..., up to the nth term — is a standard identity: it always equals n2. This holds because consecutive odd numbers form an arithmetic progression with first term 1 and common difference 2, and summing that progression algebraically reduces to a perfect square of the term count.

Applying this here:

1. The number of terms to sum is n = 95 (the first 95 odd natural numbers).

2. By the formula, the required sum is 952.

3. Computing the square: 95 × 95 = 95 × 90 + 95 × 5 = 8550 + 475 = 9025.

This can be verified independently using the arithmetic-series sum formula, Sum = (n/2) × (first term + last term). The 95th odd number (the last term) is 2 × 95 − 1 = 189, so Sum = (95/2) × (1 + 189) = (95/2) × 190 = 95 × 95 = 9025 — the same result.

Hence, the sum of the first 95 odd natural numbers is 9025.