Mathematics, 02.02.2020 17:56 kenzye32
Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth term is 54?
Answers: 3
![\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&\underline{\qquad }\\&\\ a_2&6\\&\\ a_3&\underline{6(r)}\\&\\ a_4&6(r)(r)\\&\\ &54\\ \cline{1-2} \end{array}\qquad \implies \begin{array}{llll} 54=6r^2\implies \cfrac{54}{6}=r^2\implies 9=r^2\\\\ \sqrt{9}=r\implies 3=r \end{array} \\\\[-0.35em] ~\dotfill\\\\ a_1=6\div 3\implies a_1=2~\hfill a_3=6(3)\implies a_3=18](/tpl/images/0493/4789/cef7a.png)
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Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth...
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