Question

20 PTS What is the sixth term of the sequence shown in the table? Term Value 1 –46,656 2 7,776 3 –1,296 4 216 5 6 {SEE IMAGE}

Answer 1

Answer:

a₆ = 6

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = $\frac{216}{-1296}$ = $\frac{-1296}{7776}$ = $\frac{7776}{-46656}$ = - $\frac{1}{6}$

This indicates the sequence is geometric.

To obtain any term in the sequence, multiply the previous term by r, thus

a₅ = 216 × - $\frac{1}{6}$ = - 36

a₆ = - 36 × - $\frac{1}{6}$ = 6