Answer:
a₆ = 6
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r = [tex]\frac{216}{-1296}[/tex] = [tex]\frac{-1296}{7776}[/tex] = [tex]\frac{7776}{-46656}[/tex] = - [tex]\frac{1}{6}[/tex]
This indicates the sequence is geometric.
To obtain any term in the sequence, multiply the previous term by r, thus
a₅ = 216 × - [tex]\frac{1}{6}[/tex] = - 36
a₆ = - 36 × - [tex]\frac{1}{6}[/tex] = 6
