Question

Jorge's starting annual salary is $36,500. At the beginning of each new year, he receives a $2,375 raise. Write an explicit formula to represent his salary after n years

Answer 1

Answer:

The explicit formula which represents his salary after n years is

$a_{n}$ = 2375 n + 34125

Step-by-step explanation:

The given is:

1. Jorge's starting annual salary is $36,500

2. At the beginning of each new year, he receives a $2,375 raise

We need to write an explicit formula to represent his salary after n years

The salary of the first year is $36500

Each year after the first year his salary will increase by $2375

Then his salary can form an arithmetic series because there is a

constant difference between each two consecutive years

The rule of the arithmetic series is $a_{n}=a_{1}+(n-1)d$, where

$a_{1}$ is the first term, d is the constant difference and n is the

position of the number in the series

∵ $a_{1}$ = 36500

∵ d = 2375

∴ $a_{n}$ = 36500 + (n - 1)(2375)

∴ $a_{n}$ = 36500 + 2375 (n - 1)

- Simplify it

∴ $a_{n}$ = 36500 + 2375 n - 2375

- Add like term

∴ $a_{n}$ = 34125 + 2375 n

The explicit formula which represents his salary after n years is

$a_{n}$ = 2375 n + 34125

Learn more:

You can learn more about series in brainly.com/question/7027848

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