Question

Write a recursive formula for each sequence given or described below.

Doug accepts a job where his starting salary is $30,000 per year, and each year he receives a raise of $3,000.

Answer 1

`a_(n) =a_(n-1) +3000` and a₁ =30000 for n = 2,3,4,5,6, ......

Explanation:

Doug has joined a job with a starting salary of $30000 per year.

Hence, if a₁ is the salary of Doug in the first year, then

a₁ =30000

Now, each year Doug will receive a raise of $3000 in his salary.

Hence, in the 2nd year, his salary(a₂) will become ( a₁ +3000) per year.

Again, in the 3rd year, his salary(a₃) will become ( a₂ +3000) per year.

Therefor, in the similar manner the recursive formula for his salary in each year will be given as
`a_(n) =a_(n-1) +3000` and a₁ =30000 for n = 2,3,4,5,6, ...... {aₙ is the yearly salary of Doug in the nth year} (Answer)