For the following sequences, write down the indicated term:
The third term in the sequence: 2, - 4 , 6, - 8 , 16, \ldots
The fourth term in the sequence: 3, 3.5, 4, 4.5, 5, 5.5, \ldots
The fifth term in the sequence: 5, 4, 3, 2, 1, 0, - 1 , \ldots
T_3 in the sequence: 4, - 5 , 6, - 7 , 8, \ldots
T_4 in the sequence: 200, 20, 2, 0.2, 0.02, \ldots
T_5 in the sequence: 1, 2.5, 4, 5.5, 7, 8.5, \ldots
For the following sequences:
Describe the recurring pattern in words.
Find the next number in the sequence.
- 1 , 1, 3, 5, 7, \ldots
64, 32, 16, 8, 4, 2, \ldots
2, - 4 , 6, - 8 , 10, - 12 , \ldots
Calculate:
T_2 + T_4 for the sequence: 3, 5 , 7, 9 , 10, \ldots
2 T_1 - T_5 for the sequence: 8, 5, 2, -1, -4, \ldots
- 2 \left(T_3 + T_4\right) for the sequence: -2, 4, -6, 8, -10, 12, \ldots
State whether the following are recurrence relations:
Write the recursive rule from the following descriptions. Let t_n be the nth term.
To find the next term, add 5 to the previous term.
To find the next term, add the two previous terms.
To find the next term, multiply the previous term by negative 1 and then add 7.
To find the next term, subtract one and a half from the previous term.
To find the next term, subtract 6 from the previous term.
To find the next term, multiply the two previous terms.
To find the next term, multiply the previous term by negative 5 and then subtract3.
To find the next term, add three and a quarter to the previous term.
Using the following recursive rules, state the first 5 terms of the sequence in order:
t_{n+1} = 2 t_n, t_1 = 2
a_n = a_{n - 1} + 6, a_1 = - 8
b_n = - b_{n - 1} + 3, b_1 = 0
For the following recursive relations, find:
T_2
T_3
T_4
T_n = \left( - 1 \right)^{n + 1} T_{n - 1}, T_1 = 2
T_{n + 1} = \left( 2 T_n\right)^{n - 1}, T_1 = 3
State whether the following are explicit relations:
Using the following explicit rules, state the first 5 terms of the sequence in order, starting with n = 1:
b_n = 5 n - 2
s_n = n^{2} + 6
t_n = 2 n^{2} + n - 3
Consider the sequence given in the table below:
Use the general rule to find T_{10}
| n | 1 | 2 | 3 | 4 | ... |
|---|---|---|---|---|---|
| T_n | 3 | 6 | 9 | 12 | ... |
Consider the sequence given in the table below:
Use the general rule to find T_{11}
| n | 1 | 2 | 3 | 4 | ... |
|---|---|---|---|---|---|
| T_n | 1 | 3 | 5 | 7 | ... |