Question

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 =

Answer 1

Step-by-step explanation:

The general formula of a geometric sequence is as follows:

`\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) \\ (17)/((-5)^7)\text{ = a} \\ a\text{ = -0.0002176} \end{gathered}`
`\begin{gathered} a_(12)\text{ = }(17)/((-5)^7)*(-5)^(11) \\ \text{ =10625} \end{gathered}`

Answer: 10625