Question

Find the sum of all natural numbers from 48 to 99.

• A. 3822
• B. 3922
• C. 3969
• D. 3725
• E. 3229

Answer 1

The Correct Option is A

Step 1: Understand the problem.
We are asked to find the sum of all natural numbers from 48 to 99. The sum of natural numbers in a specific range can be calculated using the formula for the sum of an arithmetic series.

Step 2: Identify the terms of the arithmetic series.
The natural numbers from 48 to 99 form an arithmetic series where:
- The first term \( a = 48 \)
- The last term \( l = 99 \)
- The common difference \( d = 1 \) (since the numbers are consecutive)

Step 3: Use the formula for the sum of an arithmetic series.
The formula for the sum \( S_n \) of the first \( n \) terms of an arithmetic series is:
\[ S_n = \frac{n}{2} \times (a + l) \] where \( n \) is the number of terms, \( a \) is the first term, and \( l \) is the last term.

Step 4: Calculate the number of terms \( n \).
The number of terms in the series from 48 to 99 is given by:
\[ n = l - a + 1 = 99 - 48 + 1 = 52 \]

Step 5: Calculate the sum of the series.
Now we can calculate the sum using the formula:
\[ S_{52} = \frac{52}{2} \times (48 + 99) = 26 \times 147 = 3822 \]

Step 6: Conclusion.
The sum of all natural numbers from 48 to 99 is 3822.

Final Answer:
The correct option is (A): 3822.