Answer:
Step-by-step explanation:
The population will increase by 2 each year. This means that the sequence is an arithmetic progression.
The formula for determining the sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
From the information given,
a = 12
d = 2 years
Therefore, the explicit rule for the sequence that models this situation: would be
Sn = n/2[2 × 12 + (n - 1)2]
Sn = n/2[24 + 2(n - 1)]
For the next 50 years, n = 50
S50 = 50/2[2 × 12 + (50 - 1)2]
S50 = 25[24 + 98)
S50 = 3050
