## Geometric Sequences Exercise

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?