Answered: 50 E(-4i) i=1

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 2CT

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Write out the first three terms and the last term (see attachment). Then use the formula for the sum of the first n terms of a_n arithmetic sequence to find the indicated sum.

Expert Solution

Given,

$\sum_{i = 1}^{50} (- 4 i)$

Put $i = 1$ , we get

$\begin{array}{rcl} a_{1} & = & - 4 (1) \\ = & - 4 \end{array}$

Put $i = 2$ , we get

$\begin{array}{rcl} a_{2} & = & - 4 (2) \\ = & - 8 \end{array}$

Put $i = 3$ , we get

$\begin{array}{rcl} a_{3} & = & - 4 (3) \\ = & - 12 \end{array}$

Put $i = 50$ , we get

$\begin{array}{rcl} a_{50} & = & - 4 (50) \\ = & - 200 \end{array}$

Therefore the first three terms are $- 4, - 8 & - 12$ and the last term is $- 200$ .

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