Part 1: Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosing a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary. Procedures: 1. Use the provided information to identify each of Mr. Nicholson's earning opportunities as arithmetic or geometric. For each opportunity, include all the common difference or ratio. 2. Model each of Mr. Nicholson's salary options with a recursive model that includes his potential earnings for the first three years of employment. a. $60,000 salary with an annual raise of $3,500 b. $60,000 salary with an annual raise of 5% of his current salary 3. Suppose Mr. Nicholson plans on working for his new employer for at least 9 years. use each of the recursive models to determine Mr. Nicholson plans on working for his new employer for at least 9 years. Use each of the recursive models to determine Mr. Nicho

Answer:See belowStep-by-step explanation:1. Arithmetic: Add 3,500The annual raise of 3,500 means add 3,500 to the previous year's salary60,000 + 3,500 = 63,50063,500 + 3,500 =  67,00067,000 + 3,500 = 70,50070,500 + 3,500 = 74,00074,000 + 3,500 = 77,500Geometric: Multiply by 1.05The annual raise by 5% of his current salary means multiply by 1.05.60,000 x 1.05 = 63,00063,000 x 1.05 = 66,15066,150 x 1.05 = 69,457.5069,457.50 x 1.05 = 72,930.38 rounded72,930.375 x 1.05 = 76,576.89The first sequence is arithmetic because we add the same number (3,500) to the preceding term. The second sequence is geometric because we multiply the preceding term by the same number always (1.05.)2a. Arithmetic - New salary is $3,500 greater each year than last year's salaryS = 60,000 + 3500(n-1)Geometric - New salary is 5% more each year than last year's salary60,000 + (1.05)^(n-1)2b. Arithmetic Earnings over 3 years60,000 + 63,500 + 67,000 = 190,500Geometric Earnings over 3 years60,000 + 63,000 + 66,150 = 189,150There is a 1,000 dollar difference. In this case, the arithmetic increase of 3,500 dollars would be better for Mr. Nicholson. 1,000 dollars may or may not be considered a big difference. In my opinion, I'd say there is a slight difference between the two3.Arithmetica(9) = 3,500 + a(9-1)a(9) = 3,500 + 89,000a(9) = 92,500Geometrica(9) = 1.05 x a(9-1)a(9) = 1.05 x 84,425.90a(9) = 88,647.204. In this case, both the 3 year and 9 year time frames favor the arithmetic increase of $3,500. At 3 years, he would have 190,500 compared to the geometric salary of 189,150. However, this is a small difference. If he is going to be at the company for 9 years, then definitely he should choose the first opportunity. 92,500 is significantly more money than 88,647.20. So, longer time frames only make the first opportunity, which is better to begin with, shine even more.I'm always happy to help :)