State the first five terms of the following sequences:
a_0 = 7 and a_{n + 1} = a_n + 5
a_0 = 2 and a_{n + 1} = 4 a_n
a_0 = 3 and a_{n + 1} = 3 a_n - 3
a_0 = 54 and a_{n + 1} = \dfrac{1}{3} a_n
a_0 = 2 and a_{n + 1} = 0.5 a_n - 7
Consider the sequence represented in the table:
Is this an arithmetic or geometric sequence?
Find x_{10}.
| n | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| x_n | -23 | -27 | -31 | -35 | -39 |
Consider the sequence represented in the table:
Is this an arithmetic or geometric sequence?
Find a_2.
| n | -3 | -2 | -1 | 0 | 1 |
|---|---|---|---|---|---|
| a_n | 2 | 1 | \dfrac{1}{2} | \dfrac{1}{4} | \dfrac{1}{8} |
Complete the sequences in the following tables:
x_n is arithmetic
| n | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|
| x_n | 4 | 12 |
y_n is geometric
| n | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|
| y_n | 4 | 12 |
Write a recursive rule, a_{n + 1}, in terms of a_n and the initial term a_0 for the following sequences:
- 4 , 6, 16, 26, \ldots
7, 13, 19, 25, \ldots
- 6 , - 4 , - 2 , 0, \ldots
- 9 , - 27 , - 81 , - 243 , \ldots
10, - 30 , 90, - 270 , \ldots
- 405 , 135, - 45 , 15, \ldots
7, \dfrac{63}{2}, \dfrac{567}{4}, \dfrac{5103}{8}, \ldots
3 , - 14 , 71, - 354 , \ldots
a_n = 4 + 5 n
a_n = - 17 \left( - 3 \right)^{n - 1}
Consider the sequence: 21, 14, 7, 0, \ldots
Write a recursive rule for a_{n+1} in terms of a_n and an initial condition for a_0.
Consider the sequence: 3000, 600, 120, 24, \ldots
Write a recursive rule, T_{n + 1}, in terms of T_n and the initial term T_0.
Each term in a sequence is obtained by subtracting 6 from the previous term. The first term is 10. Write a recursive rule, T_{n + 1}, in terms of T_n and the initial term T_0 for this sequence.
Each term is obtained by increasing the previous term by 25. The first term is 30. Write a recursive rule for T_{n+1} in terms of T_n and an initial condition for T_0 for this sequence.
Consider the sequence: a_{n + 1} = 2 a_n + 3. If a_2 = 61, find a_0.
The first term of a geometric sequence is 6. The fourth term is 384.
Find the common ratio, r, of this sequence.
State the recursive rule, T_{n+1}, that defines this sequence.
The third term of a geometric sequence is 16. The sixth term is 128.
Find the common ratio, r, of this sequence.
Find the first term of this sequence.
State the recursive rule, T_{n+1}, that defines this sequence.
The first term of a geometric sequence is 8. The third term is 128.
Find the possible values of the common ratio, r, of this sequence.
State the recursive rule, U_{n + 1}, that defines the sequence with a positive common ratio, and the initial term U_0.
State the recursive rule, T_{n + 1}, that defines the sequence with a negative common ratio, and the initial term T_0.
The third term of a geometric sequence is 8100. The seventh term is 100.
Find the possible values of the common ratio, r, of this sequence.
State the first term of this sequence.
State the recursive rule, T_{n + 1}, that defines the sequence with a positive common ratio, and the initial term T_0.
State the recursive rule, A_{n + 1}, that defines the sequence with a negative common ratio, and the initial term A_0.
For each sequence plot below:
State the first five terms of the sequence.
Is the sequence arithmetic or geometric?
Write a recursive rule, T_{n + 1}, in terms of T_n and the initial term T_0 for the sequence.
Consider the sequence: 4, 6, 8, 10, 12, \ldots
Plot the points on a coordinate plane.
Is the sequence arithmetic or geometric?
Write a recursive rule for t_{n+1} in terms of t_n and an initial condition for t_0.
Consider the sequence: 2, 6, 18, 54, \ldots
Plot the first four terms on a coordinate plane.
Is the sequence arithmetic or geometric?
Write a recursive rule for T_{n+1} in terms of T_{n} and an initial condition for T_0.
Consider the sequence: 40, 20, 10, 5, \text{. . .}
Plot the first four terms on a coordinate plane.
Is the relationship depicted by this graph linear, geometric?
State the recurrence relationship, T_{n+1}, in terms of T_n , that defines this sequence.
Consider the sequence: 3, -6, 12, -24, \ldots
Plot the first four terms on a coordinate plane.
Is the relationship depicted by this graph arithmetic, geometric?
State the recurrence relationship, A_{n+1}, in terms of A_n , that defines this sequence.
Consider the first-order recurrence relationship defined by T_{n + 1} = 3 T_n, \, T_0 = 1.
Determine the next three terms of the sequence from T_1 to T_3.
Plot the first four terms on a coordinate plane.
Is the sequence generated from this definition arithmetic or geometric?
Consider the first-order recurrence relationship defined by the following:
Determine the next four terms of the sequence, from T_1 to T_4.
Plot the first five terms on a coordinate plane.
Is the sequence generated from this definition arithmetic or geometric?
T_{n + 1} = T_n + 3, T_0 = 5
T_{n+1} = T_n - 2, T_0 = 5