Solve the problem.
-The yearly salary for job A is $57,000 initially with an annual raise of $3,200 every year thereafter. The yearly salary for job B is $53,000 initially with an annual raise of 5%.
a. Consider a sequence representing the salary for job A for year n. Is this an arithmetic or geometric Sequence? Find the total earnings for job A over 20 years. Round to the nearest dollar.
b.Consider a sequence representing the salary for job B for year n. Is this an arithmetic or geometric Sequence? Find the total earnings for job B over 20 years. Round to the nearest dollar.
A) a. Geometric; $\$ 2,011,827$
b. Geometric; $\$ 1,752,496$
B) a. Geometric; $\$ 2,011,827$
b. Arithmetic; $\$ 1,643,500$
C) a. Arithmetic; $\$ 1,748,000$
b. Geometric; $\$ 1,752,496$
D) a. Arithmetic; $\$ 1,748,000$
b. Arithmetic; $\$ 1,643,500$

Question

Solve the problem.
-The yearly salary for job A is $57,000 initially with an annual raise of $3,200 every year thereafter. The yearly salary for job B is $53,000 initially with an annual raise of 5%.
a. Consider a sequence representing the salary for job A for year n. Is this an arithmetic or geometric Sequence? Find the total earnings for job A over 20 years. Round to the nearest dollar.
b.Consider a sequence representing the salary for job B for year n. Is this an arithmetic or geometric Sequence? Find the total earnings for job B over 20 years. Round to the nearest dollar. 
A) a. Geometric; $\$ 2,011,827$
b. Geometric; $\$ 1,752,496$
B) a. Geometric; $\$ 2,011,827$
b. Arithmetic; $\$ 1,643,500$
C) a. Arithmetic; $\$ 1,748,000$
b. Geometric; $\$ 1,752,496$
D) a. Arithmetic; $\$ 1,748,000$
b. Arithmetic; $\$ 1,643,500$

Quizplus · Accepted Answer

a. Job A's salary increases by a fixed amount ($3,200) annually, making it an arithmetic sequence. The total earnings over 20 years can be calculated using the formula for the sum of an arithmetic series: $S_n = \frac{n}{2}[2a + (n-1)d]$, where $n = 20$, $a = 57000$, and $d = 3200$. This gives $S_{20} = \frac{20}{2}[2(57000) + (20-1)3200] = 10[114000 + 60800] = 10[174800] = 1748000$.b. Job B's salary increases by a percentage (5%) annually, making it a geometric sequence. The total earnings over 20 years can be calculated using the formula for the sum of a geometric series: $S_n = a\frac{1-r^n}{1-r}$, where $a = 53000$, $r = 1.05$, and $n = 20$. This gives $S_{20} = 53000\frac{1-1.05^{20}}{1-1.05}$, which approximates to \$1,752,496 when calculated.

Solve the Problem $2,011,827\$ 2,011,827$2,011,827 B Geometric; $1,752,496\$ 1,752,496$1,752,496 B) A Geometric; $2,011,827\$ 2,011,827$2,011,827

Solve the Problem $\$ 2,011,827$ B Geometric; $\$ 1,752,496$ B) A Geometric; $\$ 2,011,827$