In an arithmetic series having 50 terms, the first and last terms are 3 and 199, respectively. What is the sum of the series ?

The correct option is 5050.

To find the sum of an arithmetic series, we can use the standard formula for the sum of the first $n$ terms of an arithmetic progression (AP):

$S_n=\frac{n}{2}(a+l)$

where:
• $n$ is the total number of terms,
• $a$ is the first term, and
• $l$ is the last term.

From the given problem, we have the following values:
• Number of terms, $n=50$
• First term, $a=3$
• Last term, $l=199$

Now, let's substitute these values into the sum formula:

$S_{50}=\frac{50}{2}(3+199)$

Simplify the fraction outside the parentheses:

$S_{50}=25\times (3+199)$

Add the terms inside the parentheses:

$3+199=202$

Multiply the result by 25:

$S_{50}=25\times 202$

$S_{50}=5050$

Therefore, the sum of the arithmetic series is 5050.