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

A. -1458 B. -1558 C. -1568 D. -1664 Answer: Option B
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Solution(By Apex Team)

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

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