The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
-The following table shows a country's population from 1995 to 1998: $$\begin{array} { l | l l l }
\text { Year } & 1995199619971998 \
\hline \text { Population in millions } & 12.2012 .8113 .4514 .12
\end{array}$$ Divide the population for each year by the population in the preceding year. Use this ratio to write the general term of the geometric sequence describing the country's population growth n years after 1994. Then estimate the country's population, in millions, in 2005.
A) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.05 ) ^ { \mathrm { n } - 1 ; 19.87 \text { million } }$
B) $a _ { n } = 12.20 ( 1.05 ) ^ { n - 1 ; } 20.87$ million
C) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.04 ) ^ { \mathrm { n } - 1 } ; 24$ million
D) $a _ { n } = 12.20 ( 1.04 ) ^ { n - 1 ; 22.43 \text { million } }$

Question

The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
-The following table shows a country's population from 1995 to 1998: $$\begin{array} { l | l l l } 
\text { Year } & 1995199619971998 \
\hline \text { Population in millions } & 12.2012 .8113 .4514 .12
\end{array}$$ Divide the population for each year by the population in the preceding year. Use this ratio to write the general term of the geometric sequence describing the country's population growth n years after 1994. Then estimate the country's population, in millions, in 2005. 
A) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.05 ) ^ { \mathrm { n } - 1 ; 19.87 \text { million } }$
B) $a _ { n } = 12.20 ( 1.05 ) ^ { n - 1 ; } 20.87$ million
C) $\mathrm { a } _ { \mathrm { n } } = 12.20 ( 1.04 ) ^ { \mathrm { n } - 1 } ; 24$ million
D) $a _ { n } = 12.20 ( 1.04 ) ^ { n - 1 ; 22.43 \text { million } }$

Quizplus · Accepted Answer

The sequence is geometric with a common ratio of approximately 1.05, calculated by dividing each year's population by the previous year's population. Using the formula for a geometric sequence, $a_n = a_1 \cdot r^{n-1}$, where $a_1 = 12.20$ and $r = 1.05$, the population in 2005 (11 years after 1994) is estimated to be 19.87 million.