Alg 2 BC U11 Day 8 - Review

1.  For the sequence 2, 6, 12, 20, 30, 42, 56, …;

a)  Write the next two terms, telling what pattern you used.

b)  Write an explicit formula expressing in terms of n.

c)  Write a recursive formula for . (This formula will include both an-1 AND n.)

d)  Find the 700th term.

2.  Find the 56th term for the arithmetic sequence with = 237 and d = -7.

3.  An arithmetic sequence has = 164 and d = -9. If = -484, find n.

4. Find the 31st term for the geometric sequence with = 17 and r = 1.2.

5. A geometric sequence has = 11 and r = 3. If = 24057, find n.

6. What is the geometric mean between 25 and 100?

7. What is the arithmetic mean between 25 and 100?

8. Evaluate

9. Write using sigma notation ¼ + 1/8 + 1/16 + 1/32 + 1/64 + …

10. Find for the arithmetic series 6 + 13 + 20 + …

11. 31161 is a partial sum of the series in #10. What partial sum is it?

12. Find for the geometric series 100 + 96 + 92.16 + …

13. One of the partial sums of the series in #12 is approximately 1850. Which partial sum is it?

14. Find the value to which the series in #12 converges.

15. Explain why the geometric series 5 + 10 + 20 + 40 + … does not converge.

16. An arithmetic sequence has a19=-8.5 and a60=-39.25. Find an explicit formula for the sequence.

17. A geometric sequence has a7 = 9/32 and a11 = 729/512. Find an explicit formula for the sequence.

18. A person takes 200 mg of a prescription antibiotic once every 4 hours. During each 4-hour period, approximately 88% of the medicine in the body is eliminated.

a) How many mg of the antibiotic are in the body

a) just after taking the third tablet? b) just after taking the sixth tablet?

c) in the long run, just after taking a tablet?

d) in the long run, just before taking a tablet?

Answers:

1 a) 72, 90 add 2 more each time to get next term

b) =n2 + n

c) =2, = +2n

d) 490,700

2. -148

3. 73

4. 4035.397…

5. 8

6. 50

7. 125/2

8. 153

9.

10. 140,500

11. 94

12. 1394.994

13. 33

14. 2500

15. r = 2 which is not between -1 and 1

16. an = 5.75 - .75n

17.

18. a) 226.88 mg b) 227.27 mg c) 227.27 mg; d) 27.27 mg.