Honors Algebra 2
Name_______________________
Sequences and Series Worksheet #2
1. a) Find S6 of the series: 8, 4, 2, …
b) Find the value of S for the series above (the infinite geometric series).
2. Find three geometric means between -3 and -768.
i
 1
20    .

 4
i1
4
3. Fund the value of
4. Find the sum, if it exists, of each infinite geometric series:
1 1 1
 ...
a) 8 + 4 + 2 + 1 + …
b) 1   
3 9 27
1
c)  1  2  4  ...
d) 64 7  48 7  36 7  ...
2
5. Write the repeating decimal, 4.238 , as a fraction.
6. For what values of x does the infinite geometric series, 1   x  1   x  1  ... , have a sum?
2
7. a) A given square has a side of length 8 inches. A sequence of squares is inscribed in it by joining the
midpoints of the sides of each preceding square. Find the total length of all the segments in the figure as
the number of squares becomes infinite.
b) Find the sum of the areas of the squares.
n
n

 1 
 1
8. If an  4  4    in a sequence, then lim  4  4      ?
n
 4  
 4

1 1 1 1
9. Answer the following questions about the sequence: 1,  , ,  , ,...
2 3 4 5
a) What is the limit?
b) Is the sequence bounded?
c) Is the sequence nonincreasing?
10. Show that there is no infinite geometric series for which a1  2 and S  1 .
11. Find the 8th term of the geometric sequence in which a2  8 x 3 y 4 and r  x 2 y 3 .
12. Find the next two terms in the sequence: 3  2 5,6  4 5,12  8 5,...
3
13. Find two values of t so that 6t , t  1, ,... is a geometric sequence.
4
14. Find three positive geometric means between 5x 3 and 80x11 .
15. The arithmetic mean between two numbers is 25 and the geometric mean between the same two
numbers is 15. Find the numbers.
16. Gary saved one dime the first day of April, two dimes the second day, three dimes on the third day
and so on. How much money did he save in the entire month of April?
17. Write in summation notation: 5 + 9 + 13 + 17 + 21 + 25
18. In a geometric sequence whose first term is 2 and common ratio is 4, there is a term, an  8192 .
What is the value of n?
19. In a geometric sequence, if an  8 and an1  4 , then an 2  ?
20. Find the sum of the nine positive geometric means between 2 and 486.
21. There is an old story that a farmer arranged to have a blacksmith shoe a horse and agreed to pay him
one kernel of corn for the first nail, two for the second nail, four for the third, and so on. If each shoe
required eight nails, about how many bushels of corn did the farmer have to deliver? (One bushel is
approximately 50,000 kernels.)
Answers:
255
3
1. a) 15 b) 16
2. -12, -48, -192 or 12, -48, 192
3. 
64
4
3
2098
4. a) 16 b)
c) undefined d) 256 7
5.
6. 0  x  2
7. a) 64  32 2 b) 128
4
495
8. 4
9. a) 0 b) Yes c) No
10. Show that r  1 which makes the sum undefined.
11. 8x15 y 22
12. 24  16 5,48  32 5
13. 2, ½
6
16. $46.50
17.
 (4n  1)
n 1
21.  85,900 bushels
18. 7
19. 32
14. 10 x5 ,20 x 7 ,40 x 9
20. 240  242 3
15. 5, 45