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)=6 r=(2)/(3) a_(1)= a_(2)= a_(3)= a_(4)= a_(5)=
Solução

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GeniProfissional · Tutor por 6 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 $a_1 = 6$ and $r = \frac{2}{3}$, we can calculate the first five terms as follows:<br /><br />$a_1 = 6$<br /><br />$a_2 = a_1 \cdot r = 6 \cdot \frac{2}{3} = 4$<br /><br />$a_3 = a_2 \cdot r = 4 \cdot \frac{2}{3} = \frac{8}{3}$<br /><br />$a_4 = a_3 \cdot r = \frac{8}{3} \cdot \frac{2}{3} = \frac{16}{9}$<br /><br />$a_5 = a_4 \cdot r = \frac{16}{9} \cdot \frac{2}{3} = \frac{32}{27}$<br /><br />Therefore, the first five terms of the geometric sequence are:<br /><br />$a_1 = 6$<br /><br />$a_2 = 4$<br /><br />$a_3 = \frac{8}{3}$<br /><br />$a_4 = \frac{16}{9}$<br /><br />$a_5 = \frac{32}{27}$
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