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?

Question

Mathematics

Eric Conway

18 March, 20:38

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?

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Answers (2)

Know the Answer?

Chana Krause · Answer 1

Chana Krause 18 March, 21:29

0

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

Cameron Miller · Answer 2

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