13.09 Geometric sequences (Extended)
Write down the next two terms for the following sequences:
4, 12, 36, \ldots
12, - 48, 192, \ldots
- 1, 8, - 64, \ldots
- 6, 9, -\dfrac{27}{2},\ldots
Consider the sequence -1, -7, -49, \ldots
Find the next term of the sequence.
Find the 5th term of the sequence.
Find the 6th term of the sequence.
Explain how the common ratio of a geometric sequence can be found.
Consider the first four terms of the following geometric sequences:
Evaluate \dfrac{u_2}{u_1}.
Evaluate \dfrac{u_3}{u_2}.
Evaluate \dfrac{u_4}{u_3}.
Hence, find u_5.
- 4 , - 8 , - 16 , - 32 , \ldots
2, - 6 , 18, - 54 , \ldots
- 64 , - 16 , - 4 , -1, \ldots
State the common ratio between the terms of the following sequences:
9, 36, 144, 576, \ldots
- 6 , - 42 , - 294 , - 2058 , \ldots
2, - 16, 128, - 1024, \ldots
- 70.4 , - 17.6 , - 4.4 , - 1.1 ,\ldots
Write the first 5 terms of the following sequences given the first term and the common ratio:
First term: - 2, common ratio: 3
First term: 1.3, common ratio: - 4.
First term: 700\,000, common ratio: 1.04.
For each of the following, write the first four terms in the geometric progression:
The first term is 6 and the common ratio is 4.
The first term is 7 and the common ratio is - 2.
The first term is 700\,000 and the common ratio is 1.04.
The first term is - 2 and the common ratio is 3.
The first term is 1.3 and the common ratio is - 4.
Find the missing terms in the following geometric progressions:
- 5, \, x, \, - 80, \, 320, \, y
a, \, b, \, \dfrac{3}{25}, \, - \dfrac{3}{125}, \, c
For each of the following pairs of terms in a geometric progression:
Find the possible values of r.
Find the value of u_1.
Find the general rule for u_n, for r \gt 0.
u_3 = 18 and u_5 = 162
u_4 = 32 and u_6 = 128