1. State whether the following sequences are geometric and if they are find the common ratio:
a. 10, 20, 40, 80, ...
b. 10, 5, 2.5, ...
c. 2, 4, 6, 8, ...
d. 100, 80, 64, 51.2, ...
e. w, w2, w3, w4, ...
f. √3, 3, 3√3, ...
g. 3, -9, 27, -81, ...
2. For each of the sequences above which are geometric, find the next two terms.
3. Find the term indicated for each of the following geometric sequences.
a. 2, 4, 8, 16, ... find the 10th term.
b. 36, 18, 9, 4.5... find the 7th term.
c. 0.5, 1, 2, 4, ... find the 15th term.
d. 3, 3.3, 3.63, 3.993, ...find the 30th term.
e. 
, ... find the 8th term.
f. √5, 5, 5√5, ... find the 9th term.
g. z, 2z2, 4z3,... find the 21st term.
4. Find the n th (general term) for the sequences:
a. 2, 4, 8, ...
b. 3, 9, 27, ...
c. 6, 3, 1.5, ...
d. q, 3q, 9q, 27q, ...
e. 16, 12, 9, ...
f. 200, -100, 50, ...
g. 6, -6, 6, -6, ...
5. If the 4th term of a geometric sequence is 4 and the 8th term is 64, find the common ratio and the first term and thus list the first four terms of the sequence.
6. If the 2nd term of a geometric sequence is 9 and the 7th term is 
, find the common ratio and the first term and thus list the first four terms of the sequence.
7. Which term of the sequence 6, 12, 24, ... is equal to 768?
8. Which term of the sequence 1, 4, 16, ...is equal to 4096?
|
9. A rugby player does 2 press-ups on the first day of training. He doubles the number of press-ups each day. How many press-ups will he be doing by the 15th day of training? |
 |
Find the sum of the following geometric sequences for the number of terms indicated.
| 10. | 4, 8, 16, 32, .. | to 10 terms |
| 11. | 2, 6, 18, 54, ... | to 8 terms |
| 12. | 14, 7, 3.5, 1.75, ... | to 10 terms |
| 13. | w, 2w², 4w³, ... | to 9 terms |
| 14. | 1.1, 1.21, 1.331, ... | to 12 terms |
| 15. | 2, -4, 8, -16, ... | to 10 terms |
| 16. | 1, -1, 1, -1, ... | to 100 terms |
| 17. | 200, 150, 112.5, ... | for 9 terms |
Find the sum to infinity of the following geometric sequences:
| 18. | 30, 15, 7.5, ... |
| 19. | 8, 2, 0.5, ... |
| 20. | 40, -10, 2.5, -0.625, ... |
21. The sum of the first 6 terms of a geometric sequence is 2912.
Find the first term if the common ratio is 3.
22. In a geometric sequence, the third term is 8 and the sixth term is 64.
a. Use simultaneous equations to find the common ratio and the first term.
b. Find the sum of the first 10 terms.
|
23. A politician says that she will give $10 to charity today and that she will add double the previous day's amount every day for a month (30 days). How much does she give to charity in total? Do you think she realised how much this would be? |
 |
24. A boy will grow in height by 5% each year for a few years. If he is now 142 cm tall, how tall will he be in 6 years time?
What is his average height over the six years?
25. The increase in height L of a tree is measured each year. The table shows some of the data collected.
| Year (after planting), n |
1
|
2
|
3
|
4
|
5
|
...
|
20
|
21
|
...
|
| Increase in height, L metres |
0.800
|
0.784
|
0.768
|
0.753
|
0.738
|
0.545
|
0.534
|
a. Explain why an arithmetic sequence is not appropriate to model the increase in height L over a long period of time.
b. Show that the data can be closely modelled using a geometric sequence.
c. Using the geometric model, give a formula for the increase L in year n.
d. The tree was 0.5 metres high when planted. Based on your model in part c. what is the height of the tree 30 years after planting?
e. If the tree grows for a very long time, what is its expected maximum height?
