Short Answer
Describe the pattern in the sequence. Find the next three terms.
1. 625, 250, 100, 40,...
2. Write a recursive formula for the sequence 4, 9, 14, 19, 24, .... Then find the next term.
3. Is the sequence Arithmetic? If so what is the common difference?
–2.4, 9.8, 22, 34.2, ...
Is the sequence geometric? If so, identify the common ratio.
4. , , , , ,...
5. Suppose you drop a tennis ball from a height of 12 feet. After the ball hits the floor, it rebounds to 75% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.
6. Write an explicit formula for the sequence 3, 2, 1, 0, –1, ... Then find .
7. Write an explicit formula for the sequence , , , , , .... Then find .
8. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria.
Hours ( n )
Number of
Bacteria
9. Is the formula
1
25
2
50
3
75
4
100
5
125
is explicit or recursive ? Find the first five terms of the sequence.
10. Find the 50th term of the sequence 5, –2, –9, –16, ...
11. Find the missing term of the arithmetic sequence 20, , 28,...
12. Find the arithmetic mean of , .
13. A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?

Find the missing term of the geometric sequence.
14. 40, , 1000, ...
15. A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?
16. Use summation notation to write the series 59 + 65 + 71 + ... for 15 terms.
, find the number of terms in the series.
17. For the series
18. For the series
19. For the series
, find the first and the last term.
, find the first and the last term.
20. Evaluate the series .
21. Justine earned $22,000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job.
Does the infinite geometric series diverge or converge? Explain.
22.
23.
Evaluate the infinite geometric series. Round to the nearest hundredth if necessary.
24.
25. 1 + 0.1 + 0.01 + ...

Write the explicit formula for the sequence. Then find the fifth term in the sequence.
26.
27. The sequence –5, 0, 5, 10, ..., 65 has 15 terms. Evaluate the related series.

SHORT ANSWER
1. Divide by 2.5; 16, 6.4, 2.56.
2.
3. yes, 12.2
4. yes,
5. 5.1 feet
6. ; –10
7.
8.
9. explicit; 0, –8, –24, –48, –80
10. –338
11. 24
12.
13. 120 cartons
14. 200
15. 12 feet
; 29
16.
17. 5 terms
18. 6, 10
19. 9, 27
20. 264
21. $119,159.10
22. It converges; it has a sum.
23. It diverges; it does not have a sum.
24. 21.33
25. 1.11
26. ; 0.972
27. 450