What is the sum of the following series? -64, -66, -68, ..... , -100 Choices:
A) -1458 B) -1558 C) -1568 D) -1664 E) None of the above
Step by step solution   The sequence is -64, -66, -68, ..... -100.   The given set of numbers are in an arithmetic progression.   Key Data: First term is -64. The common difference is -2. The last term is -100.   Sum of the first n terms of an AP = n/2[2a1+(n−1)d]   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.   Step to compute number of terms of the sequence   an = a1 + (n - 1)d   -100 = -64 + (n - 1)(-2)   Therefore, n = 19.   Sum Sn = 19/2[2(−64)+(19−1)(−2)]   Sn = 19/2[−128−36]   Sn = 19 * (-82) = -1558   The correct answer is Choice -1558.
<result>B</result>
What is the sum of the following series? -64, -66, -68, ..... , -100