Alg 2 Trig H Series and Sequences Study Guide

1. Write a general term (an) for the sequence:

a. 3 4 5, , ,...

4 5 6 b. 3, 15,75, 375− − c. 2 3 4 5

, , , ,...3 4 5 6

2. Write each series using summation notation with the summing index k starting at k = 1.

a. 9 16 25 36− + − + b. 2 3 4 5 6

1 1 1 1 1

2 2 2 2 2+ + + + c. 1 1 1 1 1 1

12 3 4 5 6 7

− + − + − +

3. Given the following sequences, write both the EXPLICIT and RECURSIVE formulas.

a. 12, 4,4,12,20,....− − b. 3,3,12,48,...

4 c. 2, 10,50, 250− −

4. Find the 87th term in an arithmetic sequence with 1 4a = and d = - 5 .

5. Find the 15th term in an geometric sequence with 2 7a = and r = 2

6. Find the 13th term of:

a) a geometric sequence with: 3 3a = and 7 768a =

b) an arithmetic sequence with: 5 16= −a and 11 14=a

7. Which series Arithmetic and Geometric series converge and which diverge? Why? 8. Consider the following Geometric Series Formulas. What is the difference and how do I get from the first to the second and why?

1(1 )

1

n

na r

Sr

−=−

, 1

1

aS

r∞ =−

9. First determine if the series is arithmetic or geometric, or neither. Then, find the indicated sum.

a. 8

1

18

4

k

k=

∑ b. ( )

41

1

1 (4 1)−

=

− +∑ k

k

k

c. ( )25

k 1

7 2k=

−∑ d. +∞

=

−

∑k 1

k 1

1

2

10. Find the sum of the positive multiples of 3 from 4 to 99 (inclusive)

11. Find the sum of all even integers from 5 to 42.

12. Rewrite the repeating decimal as the ratio of 2 integers: .87

13. Careful here!!! ☺ Find: 40

7

3 2( 1)k

k=

− + −∑

14. Determine the summation of the following series: a. 22 + 18 + 14 + . . . + -26 b. 28 14 7 . . . .875+ + + +

15. In a geometric series with r = 4 and a2 = 24, which term (n) would have the value an = 6291456

16. Find n: 1

8 12 320=

− =∑n

k

k

17. In a stadium the number of seats in each row often lessens as you go from the bottom to the top. For example, in one section of a stadium the first row has 68 seats, the second row has 62 seats, the third row has 56 seats and so on following this pattern. How many rows are in this section of the stadium and how many seats are in the last row?

18. Susie has been studying really hard in Chemistry this semester and she has noticed a trend in her test grades. Each test she takes is 2.5% better than the previous test. She got a 75% on the first test of the semester and there are 6 total tests. What grades did she get on each of these tests?

19. A bouncy ball is dropped from the top of Hinsdale Central, 20 feet above the ground. It hits the ground and and bounces 62% of its original height on each subsequent bounce.

a. What is the total distance that the ball travels when it hits the ground for the 7th time?

b. What is the total distance that the ball travels before it stops?

20. The bob of a pendulum swings through an arc 36 in long on its first swing. If each successive swing is approximately 4/5 of the length of the preceding swing, how far will the bob travel before coming to rest?