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)   (Show Source): You can put this solution on YOUR website!

, with initial population .

This is an sequence, with an initial term of and a common difference of
Then:








an explicit formula is:
......,

Use your explicit formula to find
=>





Answer by ikleyn(52779)   (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  = 20 + (n-1)*35  does    work now - it should be modified.


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


Again, your correct explicit formula is   = 20 + n*35.


You can    it:   = 20 + 1*35 = 20 + 35 = 55.


In particular,   = 20 + 100*35 = 3520.

Solved.

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

----------------

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.



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