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Review of Sequences - Homework an a1 (n 1)d Sn n (a1 an ) 2 an a1r n 1 Sn a1 (1 r n ) 1 r r A P 1 n nt 1) What is the eighth term of the Fibonacci sequence? 2) What is the 7th term of the sequence defined as follows: The first term is 9 and an 5an1 3 n2? 3) What is the 18th term of an arithmetic sequence when the first term is 4 and the common difference is 7? You must use a formula. for 4) For the sequence 2, 7, 12, 17,… a) Write a formula for the nth term. b) Find the 18th term of this sequence: You must use a formula. 5) What is the sum of the first 70 terms of an arithmetic sequence when the first term is 15 and the common difference is 3? You must use a formula. 6) Find the sum of the first 60 terms of this sequence: You must use a formula. 12, 19, 26, 33… 7) Find this sum. You must use a formula. 8) What is the 12th term of a geometric sequence when the first term is 4 and 60 the common ratio is 3? You must use a 6i formula. i 1 9) For the sequence 3, 12, 48, 192,… a) Write a formula for the nth term. 10) Find the sum of the first 12 terms of this sequence: You must use a formula. 5, 10, 20, 40,… b) Find the 8th term of this sequence: You must use a formula. 11) Find this sum. You must use a formula. 12) A job pays a salary of $36,000 the first 8 year. During the next 5 years, the 3( 4)i salary increases by 2% each year. What i1 is the total salary paid over the 5 year period? Round your answer to the nearest dollar. You must use a formula. 13) Use the graphs of the arithmetic sequences {an } and {bn } to find a15 b14 14) Projections for the U.S. population, ages 85 and older, are shown in the following table. a) Divide the population for each decade by the population in the preceding decade. Show that the projected population is approximately a geometric sequence. b) Write the general term of the geometric sequence describing the U.S. population ages 85 and older, in millions, n decades after 2000. c) Use the model in part b) above to project the U.S. population, ages 85 and older, in 2090.