## College Algebra 7th Edition

$a_6=-648$
To find the sixth term, the value of the common ratio $r$ is needed. The value $r$ can be found by dividing the second term by the first term of the sequence. Thus, $r=\dfrac{a_2}{a} \\r=\dfrac{-\frac{1}{2}}{\frac{1}{12}} \\r=-\dfrac{1}{2} \cdot \dfrac{12}{1} \\r=-\dfrac{12}{2} \\r=-6$ The sixth term can be found by multiplying the common ratio $r$ to the second term four times: $a_6 = a_2 \cdot r \cdot r \cdot r \cdot r \\a_6=a_2 \cdot r^4 \\a_6 = -\dfrac{1}{2} \cdot (-6)^4 \\a_6 = -\dfrac{1}{2} \cdot 1296 \\a_6=-648$