Answer:
Tₙ=arⁿ⁻¹
T₅ = 3986
Step-by-step explanation:
In the first year, 1200 people participated.
If the number of residents who will participate is expected to increase by 35% each year,
It means the number of participants next year = 135% of the previous year = 1.35
This us an example of a geometric progression(G.P.) since the next term is gotten from the previous term by multiplication with a common constant 1.35.
The explicit rule that can be used to determine the number of people that will participate at any time is determined by the nth term of a G.P.
Nth term of a G.P., Tₙ=arⁿ⁻¹
Where First term, a =1200
Common ratio, r= 1.35
Tₙ=arⁿ⁻¹
Tₙ=1200 X 1.35ⁿ⁻¹
In the fifth year,
T₅=1200 X 1.35⁵⁻¹ = 1200 X 1.35⁴ = 3985.8075 = 3986 ( to the nearest whole number).
3986 people will participate in the fifth year.
