Answer:
Step-by-step explanation:
Since the number of streetlights in a town is growing linearly, the street lights are increasing in arithmetic progression.
The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
For n = 0, T0 = 130, therefore,
130 = a + (0 - 1)d
130 = a - d - - - - - - - - - -1
For n = 4, T4 = 154, therefore,
154 = a + (4 - 1)
154 = a + 3d - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
- 24 = - 4d
d = - 24/- 4 = 6
Substituting d = 6 into equation 1, it becomes
130 = a - 6
a = 130 + 6 = 136
a) The explicit formula for the number of lights in n months is
Tn = 136 + 6(n - 1)
b) The number of months that it will take to reach 200 lights is
200 = 136 + 6(n - 1)
200 - 136 = 6(n - 1)
64 = 6(n - 1)
6n - 6 = 64
6n = 64 + 6 = 70
n = 70/6 = 11.66
Approximately 12 months
