plz provide answer of alll parts (iv)(v)(vi) for part c of q3 (i) Determine a recurrence relation for tn. +(ii) Identify whether t₁, t2, t3,... is an arithmetic sequence, geometric sequence, or quadratic sequence.(iii) Find an explicit formula for tn, clearly justifying why your formula is correct.(iv) Determine t15, your salary in the final year of your contract.(v) Determine a formula for the series Sn = t₁+t₂ +t3+...+ tn, which will be a function of n. Clearlyshow the steps in your calculation, and simplify your formula as much as possible.(vi) Determine S15, the cumulative amount you will have been paid after you complete your 15-yearcontract.Note: to answer item (v) above, apply one of the formulas you proved in Problem #2. The job is such a perfect fit that you and your new CEO agree to a 15-year contract. You won't bemaking as much money as the recent contract signed by professional football player Patrick Mahomes(503 million dollars over 12 years), but thankfully your job description does not include being chased andtackled by 300-pound linemen!Let to be your annual salary in your nth year at the company, expressed in dollars.Your new boss offers you a starting salary of $100,000, with three different options for salary increasesthroughout your 15-year contract at this company.(a) Each year your salary is increased by $5,000. Thus, your salary for your first four years aret₁ = 100, 000, t2 = 105, 000, t3 = 110, 000, and t4 = 115,000.-(b) Each year your salary is increased by 4%. Thus, your salary for your first four years are t₁ = 100, 000,t2 = 104, 000, t3 = 108, 160, and t = 112, 486.40.(c) Each year your salary is increased by $1,000 multiplied by the number of years you have com-pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 101, 000,t3 = 103, 000, and t4 106, 000.

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(c) Each year your salary is increased by $1,000 multiplied by the number of years you have com- pleted at the company. Thus, your salary for your first four years are t₁ = 100, 000, t2 = 101, 000, t3 = 103, 000, and t4 = 106, 000.