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.
-A football player signs a contract with a starting salary of $860,000 per year and an annual increase of 5.5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the sixth year?
A) $1,123,986
B) $1,124,567
C) $1,122,713
D) $1,126,301

Question

Quizplus · Accepted Answer

The salary sequence is geometric with a common ratio of 1.055 (5.5% annual increase). To find the salary in the sixth year, use the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 860,000$, $r = 1.055$, and $n = 6$. Calculating gives $a_6 = 860,000 \cdot 1.055^{5} \approx 1,123,986$.

The General Term of a Sequence Is Given