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Explanation:
a = 200 = first term
d = -30 = common difference
Tn = nth term
Tn = a + d(n-1)
Tn = 200 + (-30)(n-1)
Tn = 200 - 30n + 30
Tn = -30n + 230
Set Tn less than 0 and isolate n
Tn < 0
-30n + 230 < 0
230 < 30n
30n > 230
n > 230/30
n > 7.667 approximately
Rounding up to the nearest whole number gets us [tex]n \ge 8[/tex]
So Tn starts to turn negative when n = 8
We can see that,
Tn = -30n + 230
T7 = -30*7 + 230
T7 = 20
and
Tn = -30n + 230
T8 = -30*8 + 230
T8 = -10 is the 8th term
and lastly
Tn = -30n + 230
T9 = -30*9 + 230
T9 = -40 is the ninth term
Or once you determine that T7 = 20, you subtract 30 from it to get 20-30 = -10 which is the value of T8. Then T9 = -40 because -10-30 = -40.
Answer:
- 10
- 40
Step-by-step explanation:
By the 7th term you should be pretty close to 0. Let's show that.
a1 = 200
n = 7
d = - 30
t7 = a1 + (n - 1)*d
t7 = 200 + (7 -1)*-30
t7 = 200 + 6*-30
t7 = 200 - 180
t7 = 20
This is the last term that is positive. when you take 30 away from t7 you are going to be in negative territory.
t8 = 200 + (8-1) * - 30
t8 = 200 + 7 * - 30
t8 = 200 - 210
t8 = - 10
Now the 9th term
t9 = 200 + (9 - 1)*-30
t9 = 200 + 8 * - 30
t9 = 200 - 240
t9 = - 40
