Solve the problem.
-As part of her retirement savings plan, Patricia deposited $\$ 400$ 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) $\$ 1100 ; \$ 30,000$
B) $\$ 1100 ; \$ 15,000$
C) $\$ 1065 ; \$ 29,300$
D) $\$ 1065 ; \$ 14,650$

Question

Quizplus · Accepted Answer

The amount deposited each year forms an arithmetic sequence with the first term $a_1 = \$400$ and a common difference $d = \$35$. The amount deposited in the $n$th year is given by $a_n = a_1 + (n - 1)d$. For the 20th year, $a_{20} = \$400 + (20 - 1)\times \$35 = \$400 + \$665 = \$1065$. The total amount deposited over 20 years is the sum of an arithmetic series: $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$. For 20 years, $S_{20} = \frac{20}{2}[2(\$400) + (20 - 1)\$35] = 10[\$800 + \$665] = 10 \times \$1465 = \$14,650$.

Solve the Problem $400\$ 400$400 In a Bank Account During Her First Year in the Patricia

Solve the Problem $\$ 400$ In a Bank Account During Her First Year in the Patricia