Question 1175030: Consider a population that grows according to the recursive rule Pn = Pn-1+60, with initial population Po=60.
Then
P1=
P2=
Find an explicit formula for the population. The formula should involve n (lower case n)
Pn=
Use the explicit formula to find P100
P100=
Answer by ikleyn(52830)   (Show Source):
You can put this solution on YOUR website! .
This sequence is well known ARITHMETIC progression
with the first term of 60 and the common difference of 60.
Simply, the numeration is shifted one unit to the left and starts from 0 (very first term) instead of traditional 1.
The formula for the n-th term (accounting for the accepted numeration) is
P(n) = 60 + n*60 = (n+1)*60, n = 0, 1, 2, 3, . . .
To find any term (1st, 2nd, . . . , 100th), substitute the index value to the formula.
P1 = 120; P2 = 180; P100 = 101*60 = 6060. ANSWER
Solved.
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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.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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