need help solving and with good steps so i can understand

Question

Consider a population that grows according to the recursive rule , with initial population 

Then:

 = 

 = 

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

   



Use your explicit formula to find 

 = 

Answer 1

This is an arithmetic sequence, with an initial term of 40 and a common difference of 75.

accordingly,

P₁ = P₀ + 75

P₁ = 40 + 75 = 115

P₂ = P₁ + 75

P₂ = 115 + 75 = 190

P_n = P₀ + n*75 = 40 + n*75

P₁₀₀ = 40 + 100*75 = 7540