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Arithmetic and Geometric Word Problems We can find the nth term and a sum, but how does this apply to real life? 1. Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on. 2. Consider a job offer with a starting salary of $32,500 and an annual raise of $2,500. Determine the total compensation from the company through six full years of employment. 3. An investment firm has a job opening with a salary of $30,000 for the first year. Suppose that during the next 30 years there is a 5% raise each year. Find the total compensation of the 40-year period. 4. You have a job that starts out with a salary of $30,000. You have two options: 1) a 5% increase in your salary per year or 2) a $3000 raise each year. Which option would you choose? Explain. Extra Practice 1) Is the sequence arithmetic, geometric, or neither? Find the 6th term. a. 1, 4, 9, 16, … b. 40, 20, 10, 5, … c. 2, 5, 9, 14, … 2) Write a formula for the nth term. a. 2 3 4 5 , , , ,... 9 16 25 36 b. 40, 20, 10, 5, … d. 6, 14, 22, 30, … c. 6, 14, 22, 30, … 3) Write the formula for the nth term. Then find a30 a. -4, 0, 4, 8, 12, … b. 1, 2, 4, 8, … c. 8, 12, 18, 27, … (hint: part c is geometric) 4) Write the series using summation notation. a. 600 300 150 75 37.5 b. 1 4 7 10 ... 298 5) Find the first term of the sequence using the given information. a. Arithmetic: a4 10 a16 46 b. Geometric: a3 32 a10 4096 6) Find the sum of the sequence. (hint: are the rules are arithmetic or geometric?) 1 b. n 1 3 8 105 a. 3n 4 n 1 n 1 7) Find the sum of the infinite geometric sequence. a. 8, 12, 18, 27, … b. 40, 20, 10, 5, … c. 1 5 25 , , ,... 2 4 8 d. 4 3 9 ,1, , ,... 3 4 16