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Sagot :
The formula used to calculate the nth term of a geometric sequence is given to be:
[tex]a_n=a_1\cdot r^{n-1}[/tex]From the question, we are given the following parameters:
[tex]\begin{gathered} a_1=34 \\ r=-\frac{1}{2} \end{gathered}[/tex]Therefore, we can calculate the first 5 terms as follows:
First Term: 34
Second Term: -17
[tex]\begin{gathered} n=2 \\ \therefore \\ a_2=34(-\frac{1}{2})^{2-1}=34\times(-\frac{1}{2}) \\ a_2=-17 \end{gathered}[/tex]Third Term: 8.5
[tex]\begin{gathered} n=3 \\ \therefore \\ a_3=34(-\frac{1}{2})^{3-1}=34\times\frac{1}{4} \\ a_3=8.5 \end{gathered}[/tex]Fourth Term: -4.25
[tex]\begin{gathered} n=4 \\ \therefore \\ a_4=34(-\frac{1}{2})^{4-1}=34\times(-\frac{1}{2})^3=34\times(-\frac{1}{8}) \\ a_4=-4.25 \end{gathered}[/tex]Fifth Term:
[tex]\begin{gathered} n=5 \\ \therefore \\ a_5=34(-\frac{1}{2})^{5-1}=34\times(-\frac{1}{2})^4=34\times\frac{1}{16} \\ a_5=2.125 \end{gathered}[/tex]The first five terms are 34, -17, 8.5, -4.25, and 2.125.
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