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What is a possible value for the missing term of the geometric sequence? 46, ___ , 414, ...
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\[46 \times r = 414 \div r\] find the r, and then find the common ratio.
I mean then find the geometric mean...
what he said^
\(\large {\begin{array}{llll} term&value \\\hline\\ 1&46\\ 2&\square \implies 46\cdot {\color{red}{ r}}\\ 3&414\implies 46\cdot {\color{red}{ r}}\cdot {\color{red}{ r}} \end{array} \\ \quad \\ 414=46r^2\implies \cfrac{414}{46}=r^2\implies \sqrt{\cfrac{414}{46}}={\color{red}{ r}} \\ \quad \\ \square \implies 46\cdot {\color{red}{ r}} }\)
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