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Name _____________________________________ Date _____________________ Sequences and Series Quiz Review Find the first 4 terms of the sequence and determine if it is arithmetic, geometric or neither. 1. t n n 1 n 2 2. t n 3 3 2 n 1 ____, ____, ____, ____ ____, ____, ____, ____ ___________________ ___________________ Find the formula for t n and sketch the graph of each arithmetic or geometric sequence. 3. 30, 26, 22, 18,… 4. 80, 20, 5, … ______________ ________________ State whether the given sequence is arithmetic, geometric or neither. Find a formula for the nth term of the sequence. a a2 a3 a 4 , , , 9 18 36 72 5. 11, 101, 1001, 10001 … 6. _______________ _______________ _____________________ _____________________ 7. Find t12 in an arithmetic sequence 8. How many terms are in the geometric 1 1 sequence , ,..., 1 ? 32 16 for which t3 8 and t6 6 9. How many numbers between 436 and 1,288 are multiples of 5? Find the 3rd, 4th and 5th terms in each recursive sequence. 10. t1 2 , t n n t n1 11. t1 7 , t 2 3 , t n t n1 2t n2 ______, _____, _____ ______, _______, _______ 12. Give a recursive definition for the sequence 1, 3, 7, 13, 21, 31, … ____________________________________ Find the specified sum for each series. In some problems, you may need to notice what type of sequence you are given, in others you are told. 13. In an arithmetic series with t1 3 and t10 39 , find S10 . 14. 15. In a geometric series with t3 = 24 8 And t 6 , find S 7 . 9 16. Find S n in 1 + 2 + 4 + 8 + … + t n . -1 + 4 + 9 + 14 +… + 999 17. Find the sum of all the multiples of 2 and 3 between 1,000 and 1,500. 18. Find the sum of the series 1 – 3 + 5 – 7 + 9 – 11 + … + 1001. Evaluate the limit. Give its numeric value, state that it is or or state that the limit does not exist. n2 1 n4 8n 2 12n 19. lim 20. lim 2 21. lim n n n 2 n 2 n 1 5n 2 1 22. lim log cos n n 23. lim n 1n1 n 2 24. lim 4 1 n n “Calculator” Problems 25. In a city with a population of 875,000 the annual birth rate is 1.5%, but 25,000 people move out each year due to a tough job market. How many years from now will the population drop below 750,000? 26. When Mr. Moneybags reaches his retirement age of 65, he expects to have a retirement account worth $850,000. One month after he retires, and every month thereafter, he intends to withdraw $8,000 from the account. The balance will be invested at 5% annual interest compounded monthly. a) Let An represent the amount of money in the account after n months. Write a recursive definition for An . b) When will he have less than $150,000 in his account? 1 2 1 3 2 1 2 3 105 27. Find ... 10 20 30 100