Answer:
a
n
=
−
16
(
−
1
4
)
n
,
n
=
{
0
,
1
,
2
,
3
,
⋯
}
Step-by-step explanation:
We have the sequence
{
−
16
,
4
,
−
1
,
⋯
}
By looking at the first three terms of the sequence, we can already see a pattern.
Starting at -16, each term has its sign reversed, and is divided by 4.
Hence the sequence can be written as:
{
−
16
,
−
16
(
−
1
4
)
,
−
16
(
−
1
4
)
2
,
⋯
}
So the formula for the
n
th term of the sequence is
a
n
=
−
16
(
−
1
4
)
n
,
n
=
{
0
,
1
,
2
,
3
,
⋯
}
