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

It's 6

Explanation:

Got it right!

1 –46,656

2 7,776

3 –1,296

4 216

5 36

6 6

divided by 6 every time

Answer 2

a₆ = 6

Explanation:

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

r =
`(216)/(-1296)` =
`(-1296)/(7776)` =
`(7776)/(-46656)` = -
`(1)/(6)`

This indicates the sequence is geometric.

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

a₅ = 216 × -
`(1)/(6)` = - 36

a₆ = - 36 × -
`(1)/(6)` = 6