Solve the problem.
-As part of her retirement savings plan, Patricia deposited $100 in a bank account during her first year in the workforce. During each subsequent year, she deposited $45 more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.
A)$955; $10,550
B)$1000; $22,000
C)$955; $21,100
D)$1000; $11,000

Question

Quizplus · Accepted Answer

The amount Patricia deposited during her twentieth year can be found using the arithmetic sequence formula: $a_n = a_1 + (n-1)d$, where $a_n$ is the amount deposited in the nth year, $a_1$ is the initial amount deposited ($100), $n$ is the year number, and $d$ is the common difference between the deposits ($45). For the 20th year: $a_{20} = 100 + (20-1)45 = 100 + 855 = $955$. The total amount deposited over 20 years can be calculated using the formula for the sum of an arithmetic series: $S_n = \frac{n}{2}[2a_1 + (n-1)d]$, where $S_n$ is the total amount deposited over n years. For 20 years: $S_{20} = \frac{20}{2}[2(100) + (20-1)45] = 10[200 + 855] = 10[1055] = $10,550$.

Solve the Problem. -As Part of Her Retirement Savings Plan, Patricia Deposited $100