Question

Consider a population that grows to the recursive rule Pn= Pn-1 + 50,

Answer 1

Answer:

a)   P₁  = 250 and    P₂ = 300

b) The explicit formula   Pₙ = 150+ 50 n

c)  $P_{60} = 3150$

Step-by-step explanation:

Step(i):-

Given that Pₙ = pₙ₋₁ +50 and P₀ = 200

Put n =1

         P₁ = P₀+50 = 200+50 = 250

Put n =2

         P₂ = P₁+50 = 250+50 = 300

Put n=3

       P₃ = P₂+50 = 300+50 = 350

and so on

The sequence     200,250,300,350,..

Step(ii):-

The sequence     200,250,300,350,.. is an arithmetic sequence

The explicit formula

       Pₙ = a+(n-1)d

       Pₙ = 200+(n-1)50

       Pₙ = 200+ 50 n -50

        Pₙ = 150+ 50 n

The explicit formula   Pₙ = 150+ 50 n

c)

The $n^{th}$ term of the sequence

       Pₙ = 150+ 50 n

put n=60

      $P_{60} = 150 + 50 (60) = 3150$