Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-A job pays a salary of 30,000 the first year. During the next 7 years, the salary increases by 4% each year. What is the salary for the 8th year? What is the total salary over the 8-year period? (Round to the nearest cent.)
A) $39,477.95; $276,426.79
B) $39,477.95; $236,948.83
C) $41,057.07; $317,483.86
D) $41,057.07; $236,973.83

Question

Quizplus · Accepted Answer

The salary for the 8th year is calculated using the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 30,000$, $r = 1.04$ (4% increase), and $n = 8$. This gives $a_8 = 30,000 \cdot 1.04^{7} \approx 39,477.95$. The total salary over the 8-year period is found using the sum formula for a geometric series: $S_n = a_1 \cdot \frac{1 - r^n}{1 - r}$, which gives $S_8 = 30,000 \cdot \frac{1 - 1.04^8}{1 - 1.04} \approx 276,426.79$.

Find the Indicated Sum