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Write the first five terms of the geometric sequence given the first term and common ratio. Leave your solutions in fraction form. a_(1)=1 r=-(1)/(2) a_(1)= a_(2)= a_(3)= a_(4)= a_(5)=

Pergunta

Write the first five terms of the geometric sequence given the first term and common
ratio. Leave your solutions in fraction form.
a_(1)=1
r=-(1)/(2)
a_(1)=
a_(2)=
a_(3)=
a_(4)=
a_(5)=

Write the first five terms of the geometric sequence given the first term and common ratio. Leave your solutions in fraction form. a_(1)=1 r=-(1)/(2) a_(1)= a_(2)= a_(3)= a_(4)= a_(5)=

Solução

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MárcioVeterano · Tutor por 9 anos

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To find the first five terms of the geometric sequence, we can use the formula:<br /><br />$a_n = a_1 \cdot r^{(n-1)}$<br /><br />where $a_n$ is the nth term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.<br /><br />Given that $a_1 = 1$ and $r = -\frac{1}{2}$, we can calculate the first five terms as follows:<br /><br />$a_1 = 1$<br /><br />$a_2 = a_1 \cdot r = 1 \cdot \left(-\frac{1}{2}\right) = -\frac{1}{2}$<br /><br />$a_3 = a_2 \cdot r = -\frac{1}{2} \cdot \left(-\frac{1}{2}\right) = \frac{1}{4}$<br /><br />$a_4 = a_3 \cdot r = \frac{1}{4} \cdot \left(-\frac{1}{2}\right) = -\frac{1}{8}$<br /><br />$a_5 = a_4 \cdot r = -\frac{1}{8} \cdot \left(-\frac{1}{2}\right) = \frac{1}{16}$<br /><br />Therefore, the first five terms of the geometric sequence are:<br /><br />$a_1 = 1$<br /><br />$a_2 = -\frac{1}{2}$<br /><br />$a_3 = \frac{1}{4}$<br /><br />$a_4 = -\frac{1}{8}$<br /><br />$a_5 = \frac{1}{16}$
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