Answer:
a) P₁ = 250 and P₂ = 300
b) The explicit formula Pₙ = 150+ 50 n
c) [tex]P_{60} = 3150[/tex]
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 [tex]n^{th}[/tex] term of the sequence
Pₙ = 150+ 50 n
put n=60
[tex]P_{60} = 150 + 50 (60) = 3150[/tex]
