Answer:
n = 15
Step-by-step explanation:
This is an
Arithmetic sequence
The sum of the first n terms of this sequence is given by.
S
n
=
n
2
[
2
a
+
(
n
−
1
)
d
]
where a is the first term and d , the common difference.
here a = -16 , d = 8 and require to solve for n.
hence :
n
2
[
(
2
×
−
16
)
+
8
(
n
−
1
)
]
=
600
n
2
[
−
32
+
8
n
−
8
]
=
600
⇒
n
2
(
8
n
−
40
)
=
600
distributing gives :
4
n
2
−
20
n
−
600
=
0
Equated to zero since this is a quadratic equation.
⇒
4
(
n
2
−
5
n
−
150
)
=
0
⇒
4
(
n
+
10
)
(
n
−
15
)
=
0
⇒
n
=
−
10
or
n
=
15
but n > 0 hence n = 15
Step-by-step explanation: