Final answer:
The sum of the given arithmetic series is 9801.
Step-by-step explanation:
The given series is an arithmetic series with a common difference of 2. To find the sum of an arithmetic series, you can use the formula: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
Using this formula, we can calculate the sum of the series:
a = 50, l = 148, d = 2, n = ?
Sn = (n/2)(a + l) = (n/2)(50 + 148) = 99n.
To find n, we can set l = a + (n-1)d:
148 = 50 + (n-1)2
n = (148 - 50)/2 + 1 = 99.
Now we can substitute n into the formula:
Sn = 99n = 99 * 99 = 9801.