<p>Two geometric sequences <img alt="$a_1, a_2, a_3, \ldots$" height="11" src="https://latex.artofproblemsolving.com/c/4/a/c4a82e7c7dbf7b035a66b5890ec80463b4c3e8d9.png" width="95" /> and <img alt="$b_1, b_2, b_3, \ldots$" height="16" src="https://latex.artofproblemsolving.com/c/c/a/cca9b5221ba4288112c1abdf85541050781f21c9.png" width="89" /> have the same common ratio, with <img alt="$a_1 = 27$" height="17" src="https://latex.artofproblemsolving.com/3/4/4/344f7d79496fb8310a89c823a6ccaf8974a11fa9.png" width="61" />, <img alt="$b_1=99$" height="15" src="https://latex.artofproblemsolving.com/9/a/9/9a9fb2278c733be5edd896d46a82eb7f1c9410cb.png" width="57" />, and <img alt="$a_{15}=b_{11}$" height="15" src="https://latex.artofproblemsolving.com/b/f/8/bf8216d866e1bbb60c6691b2ad75a42a3df283f6.png" width="68" />. Find <img alt="$a_9$" height="10" src="https://latex.artofproblemsolving.com/f/b/7/fb7904c50fdc103fee44ab630f82383c0b78febc.png" width="15" />.</p>

Question No: 307

Two geometric sequences $a_1, a_2, a_3, \ldots$ and $b_1, b_2, b_3, \ldots$ have the same common ratio, with $a_1 = 27$ , $b_1=99$ , and $a_{15}=b_{11}$ . Find $a_9$ .

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Tags: Algebra Probability

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