SOLUTION: Consider a population that grows according to the recursive rule Pn=Pn-1+35, with initial population Po=20. Then: P1 = __________ P2 = _________ Find an explicit f

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Question 1206057: Consider a population that grows according to the recursive rule Pn=Pn-1+35, with initial population Po=20.

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 =__________

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

P%5Bn%5D=P%5Bn-1%5D%2B35, with initial population P%5Bo%5D=20.

This is an arithmetic sequence, with an initial term of 20 and a common difference of 35
Then:
P%5B1%5D+=P%5Bo%5D%2B35
P%5B1%5D+=20%2B35
P%5B1%5D+=55

P%5B2%5D+=+P%5B1%5D+%2B35
P%5B2%5D+=+55+%2B35
P%5B2%5D+=+90

an explicit formula is:
P%5Bn%5D=+P%5Bo%5D%2Bd%28n-1%29......P%5Bo%5D=20, d=35
P%5Bn%5D=+20%2B35%28n-1%29
Use your explicit formula to find P%5B100%5D
=>n=100
P%5B100%5D+=20%2B35%28100-1%29
P%5B100%5D+=20%2B35%2899%29
P%5B100%5D+=3485


Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

        Be careful :   this problem is a trap.

        The trap is that this sequence is  SPECIAL :   it  IS  an arithmetic sequence,
        but starts from the zeroth term  20.

        Therefore,  the formula for the n-th term must be modified. 


The standard formula P%5Bn%5D = 20 + (n-1)*35  does  highlight%28highlight%28NOT%29%29  work now - it should be modified.


    +---------------------------------------------+
    |   The correct formula is P[n] = 20 + n*35   |
    +---------------------------------------------+


Again, your correct explicit formula is  P%5Bn%5D = 20 + n*35.


You can  CHECK  it:  P%5B1%5D = 20 + 1*35 = 20 + 35 = 55.


In particular,  P%5B100%5D = 20 + 100*35 = 3520.

Solved.

The solution and the calculations by @MathLover1 are  INCORRECT  and lead you to  WRONG  answer.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.