The correct answer is option (A):
3822
The problem asks us to find the sum of all natural numbers from 48 to 99, inclusive. We can solve this in a couple of ways.
Method 1: Arithmetic Series Formula
The sum of an arithmetic series is given by the formula: S = (n/2) * (a + l), where 'S' is the sum, 'n' is the number of terms, 'a' is the first term, and 'l' is the last term.
First, identify the values.
* a (first term) = 48
* l (last term) = 99
* To find 'n' (number of terms), we can use the formula: n = l - a + 1. So, n = 99 - 48 + 1 = 52.
Now, plug the values into the formula:
S = (52/2) * (48 + 99)
S = 26 * 147
S = 3822
Method 2: Using the sum of the first 'n' natural numbers
We can find the sum of the first 99 natural numbers, then subtract the sum of the first 47 natural numbers. The sum of the first 'n' natural numbers is given by the formula: Sum = n * (n + 1) / 2
Sum of first 99 numbers = 99 * (99 + 1) / 2 = 99 * 100 / 2 = 4950
Sum of first 47 numbers = 47 * (47 + 1) / 2 = 47 * 48 / 2 = 1128
Subtract the second sum from the first: 4950 - 1128 = 3822
Both methods lead to the same result: 3822. Therefore, the correct answer is 3822.