Arithmetic Progression

The first term of the A.P. is , and the common difference is . The general formula for the nth term of an A.P. is: Step 1: We are given that the last term is 205, so: Step 2: Simplify the equation: Thus, the number of terms in the A.P. is 34.

The odd numbers from 1 to 1001 form an arithmetic sequence where: - First term ( ) = 1 - Last term ( ) = 1001 - Common difference ( ) = 2 Step 1: Find the number of terms ( ): Step 2: Use the sum formula for an arithmetic series:
Thus, the correct sum is 251001.

The sum of first natural numbers is given by: