Question

Sum of all odd integers from 1 to 1001 is:

• A. 251001
• B. 242105
• C. 251003
• D. 261001

Hint:

The sum of the first \( n \) odd numbers is given by: \[ S_n = n^2 \] For \( n = 501 \): \[ S_{501} = 501^2 = 251001 \]

Answer 1

The Correct Option is A

The odd numbers from 1 to 1001 form an arithmetic sequence where: - First term (\( a \)) = 1 - Last term (\( l \)) = 1001 - Common difference (\( d \)) = 2 Step 1: Find the number of terms (\( n \)): \[ n = \frac{l - a}{d} + 1 \] \[ n = \frac{1001 - 1}{2} + 1 = 501 \] Step 2: Use the sum formula for an arithmetic series: \[ S_n = \frac{n}{2} (a + l) \] \[ S_{501} = \frac{501}{2} (1 + 1001) \] \[ = \frac{501}{2} \times 1002 \] \[ = 501 \times 501 = 251001 \]
Thus, the correct sum is 251001.