Name ______Date ______

REVIEW #19 – SEQUENCES AND SERIES

1.  Find the sixth term in the expansion of (2x – y)15.

2.  Find the term containing x4 in the expansion of the binomial (3x – 2y)9.

3.  Determine whether each sequence is arithmetic, geometric, or neither. Then supply the missing terms.

a) type: ______, ______, ______

b) type:______5, 17, 29, 41, ______, ______

c) type: ______2, 4, 7, 11, ______, ______

4.  Find the specified term in the sequence.

a)  1, , , …a7

b)  -4, -1.5, 1, 3.5, …a21

c)  a5 = 190 and a10 = 115. Find a20 if the sequence is arithmetic.

d)  a3 = 4 and a6 = . Find a10 if the sequence is geometric.

5.  Insert 3 arithmetic means between 24 and 56.

6.  Find the number of terms in the sequence 47, 41, 35, …, 5.

7.  Find the indicated sum for each of the following:

a) b) c)

8. Express the following series using sigma notation. -3 + 7 – 11 + 15 - …

9.  Find the sum of the indicated number of terms in each series.

a)  1.50 + 1.45 + 1.40 + 1.35 +… + a20

b)  5 – 10 + 20 - …a7

c) 

10. A new pair of running shoes costs $70 now. Assuming an annual 8% price increase, find the price 4 years from now.

11. How many rows are in the corner section of a sports complex if the first row has 18 seats and the last row has 51 seats and each successive row has one additional seat? How many seats are in the section?

12. Calvin Butterball and Phoebe Small start walking from the same point. Phoebe starts with a 12 inch step, and increases her stride by ½ inch each step. Calvin starts out with a 36 inch step, and each subsequent step is shorter by 10% than the step before.

a) Write a formula for the length of the nth step for each person.

b) Find the length of the 20th step for each person.

c) Find out who is ahead after 20 steps and by how far.

d) Will either of them have a maximum distance they will walk according to the

models? Explain. If so, find the maximum.

13. Answer the following questions for the sequence: 2, 6, 12, 20, 30, 42, …

a) Is the sequence arithmetic, geometric, or neither?

b) Write a formula for the nth term as an expression of n.

c) Find a48.

14. Write the complete binomial expansion of (4x – 5y)6.


Answers to Review #19

1.  -3075072x10y5

2.  –326,592x4y5

3.  a) geometric: 27, -27

b) arithmetic; 53, 65

c) neither; 16, 22

4.  a)

b) 46

c) -35

d) 

5.  32, 40, 48

6.  8

7.  a) 520

b)  44, 625

c)  592.647

8. 

9.  a) 20.5

b)  215

c) 

10. $95.23

11. 34 rows, 1173 seats

12. Phoebe Calvin

a) an = .5n + 11.5 an = 36(.9)n-1

b) 21.5 in 4.863 in

c) Phoebe by 18.768 in

d) Calvin will because his series is convergent. 360 in

13. a) Neither

b) an = n(n+1)

c) 2352

14. 4096x6 – 30,720x5y + 96,000x4y2 – 160,000x3y3 + 150,000x2y4 – 75,000xy5 + 15,625y6