Question: This is for a class called Discrete Mathematics. The Module is called Recurrence Relation and Logic and this is all the information that is given

This is for a class called Discrete Mathematics. The Module is called Recurrence Relation and Logic and this is all the information that is given in the paper. I must show my work in order to get full credit.

1.Your new job has a starting pay of $45,000.Each year, your boss promises you an increase of $750.With this scenario in mind, answer the following questions provided that number of years working at the company.

(a)Give the recursively-defined sequence formula using and in terms of for . (Hint: assume that is 1 year worked at your job).

(b)List the first five terms in the sequence.

(c)Find the formula that represents the sequence without using previous terms (Use the inspired guess method).

(d)If your boss changes your salary increase each year to 3% of your pay, how does the sequence change? Write the sequence as a recursively-defined sequence.Convert the formula to a formula without using previous terms.

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