Help I dont understand how to do this!!

Question

Consider a population that grows according to the recursive rule Pn=Pn−1+80, with initial population Po=80.



Then:

P1= 

P2= 

Find an explicit formula for the population. Your formula should involve n (use lowercase n)

Pn= 

Use your explicit formula to find P100

P100=

Answer 1

P_n = P_n-1 + 80 and P₀ = 80

So, P₁ = P₀ + 80 = 160 and P₂ = P₁ + 80 = 240

The sequence is 80, 160, 240, ... which is arithmetic with common difference d = 80.

P_n = P₁ + (n-1)(d) = 160 + 80(n - 1) = 80n + 80

So, P₁₀₀ = 8080