What is the sum of the following series? -64, -66, -68, ......, -100

Answer: Option B

First term is -64. The common difference is -2. The last term is -100.
Sum of the first n terms of an AP =
$$\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]$$
To compute the sum, we know the first term a1 = -64 and the common difference d = -2.
We do not know the number of terms n. Let us first compute the number of terms and then find the sum of the terms.
a_n = a₁ + (n - 1)d
-100 = -64 + (n - 1)(-2)
Therefore, n = 19
Sum =
$$S_n=\frac{19}{2}$$ $$\left[2\left(-64\right)+\left(19-1\right)\left(-2\right)\right]$$
$$\begin{array}{rl}& S_n=\frac{19}{2}\left[-128-36\right]\\ & S_n=19\times \left(-82\right)\\ & S_n=-1558\end{array}$$