Solve the problem.
-As part of her retirement savings plan, Patricia deposited $150 in a bank account during her first year in the workforce. During each subsequent year, she deposited $35 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) $850; $20,000
B) $815; $19,300
C) $815; $9650
D) $850; $10,000

Question

Quizplus · Accepted Answer

The amount deposited each year forms an arithmetic sequence with the first term $150 and a common difference of $35. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference. For the 20th year, $a_{20} = 150 + (20 - 1)35 = 150 + 665 = 815$. The sum of the first n terms of an arithmetic sequence is given by $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$. For 20 years, $S_{20} = \frac{20}{2}[2(150) + (20 - 1)35] = 10[300 + 665] = 10[965] = 9650$.

Solve the Problem. -As Part of Her Retirement Savings Plan, Patricia Deposited $150