Question

Alex earns a \$35{,}000$35,000dollar sign, 35, comma, 000 salary in the first year of his career. Each year, he gets a 3\%3%3, percent raise. Which expression gives the total amount Alex has earned in his first n years of his career?

Answer 1

Answer:35,000(1-1.03^n)/-0.03

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Each year, he gets a 3 percent raise. This means that his salary between consecutive years increasing by a common ratio. The formula for determining the sum of the first n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = 35000

r = 1 + 3/100 = 1 + 0.03 = 1.03

Therefore, the expression that gives the total amount Alex has earned in his first n years of his career is

Sn = [35000(1.03)^n - 1]/(1.03 - 1)

Sn = [35000(1.03)^n - 1]/0.03