Answer: 10
Step-by-step explanation:
Use the formula for partial sum.
S
n
=
n
2
[
2
a
1
+
(
n
−
1
)
d
]
80
=
n
2
[
2
(
−
1
)
+
(
n
−
1
)
2
]
80
=
n
2
[
−
2
+
2
n
−
2
]
80
=
n
2
[
2
n
−
4
]
80
=
n
(
n
−
2
)
80
=
n
2
−
2
n
n
2
−
2
n
−
80
=
0
Solve this quadratic equation by factoring:
n
2
−
2
n
−
80
=
0
(
n
−
10
)
(
n
+
8
)
=
0
n
=
10
;
n
=
−
8
Since the number of terms in a sequence is always positive, we conclude that 10 terms of the sequence
−
1
,
1
,
3
,
5
,
⋯
are added to obtain a sum of 80.