Question

Consider a population that grows according to the recursive rule
P
n
=
P
n
−
1
+
25
, with initial population
P
0
=
30
.

Then:

P
1
=

P
2
=


Find an explicit formula for the population. Your formula should involve
n
(use lowercase n)

P
n
=



Use your explicit formula to find
P
100


P
100
=

Answer 1

The explicit formula for the arithmetic sequence is: $P_n = 30 + 25n$

Using the formula, we have that $P_{100} = 2530$.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n - 1)d$

In which $a_1$ is the first term.

From the recursive formula, we have that:

$a_1 = 30 + 25 = 55, d = 25$

Hence the explicit formula is:

$P_n = 55 + 25(n-1)$

$P_n = 30 + 25n$

Then, when n = 100:

$P_{100} = 30 + 25(100) = 2530$

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

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