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

Solution(By Examveda Team)

First term is -64. The common difference is -2. The last term is -100.
Sum of the first n terms of an AP =
$$\frac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right]$$
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 =
$${S_n} = \frac{{19}}{2}$$ $$\left[ {2\left( { - 64} \right) + \left( {19 - 1} \right)\left( { - 2} \right)} \right]$$
$$\eqalign{ & {S_n} = \frac{{19}}{2}\left[ { - 128 - 36} \right] \cr & {S_n} = 19 \times \left( { - 82} \right) \cr & {S_n} = - 1558 \cr} $$