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For a given geometric sequence, the common ratio, r, is equal to -5, and the 8th term, ag, is equal to 17. Find the value of the 12thterm, a12. If applicable, write your answer as a fraction.a12 =
The general formula of a geometric sequence is as follows:
[tex]\begin{gathered} a_n\text{ = a*r}^{n-1} \\ We\text{ are told that the common ration r = -5 and that a}_8\text{ = 17} \\ First\text{ we will solve for a, the first term.} \\ 17\text{ = a*\lparen-5\rparen}^{8-1} \\ \frac{17}{(-5)^7}\text{ = a} \\ a\text{ = -0.0002176} \end{gathered}[/tex][tex]\begin{gathered} a_{12}\text{ = }\frac{17}{(-5)^7}*(-5)^{11} \\ \text{ =10625} \end{gathered}[/tex]
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