Use the following recursive definitions to state the first 3 terms of the sequence:
T_{n + 1} = T_n + 5, T_{1} = 4
T_n = T_{n - 1} - 4, T_{1} = - 12
T_{n + 1} = - 2.5 + T_n, T_{1} = 4
T_n = 13 + T_{n - 1}, T_{1} = 3
For the following arithmetic progressions given by the explicit rule:
Find a, the first term in the arithmetic progression.
Find d, the common difference.
Calculate T_9.
T_n = 4 + 5 \left(n - 1\right)
T_n = 2 - 6 \left(n - 1\right)
T_n = - 2 + 6 \left(n - 1\right)
T_n = - 4 - 5 \left(n - 1\right)
For each of the following sequences:
State the recursive rule for T_n in terms of T_{n - 1}, as well as the initial term T_1.
State the explicit rule for T_n in terms of n.
Calculate T_{16}.
12, 15, 18, 21, \ldots
22, 17, 12, 7, \ldots
- 20 , - 16 , - 12 , - 8 , \ldots
5, 6.5, 8, 9.5, \ldots
For each of the sequences below:
Find d, the common difference.
Write a recursive rule for T_n in terms of T_{n - 1} and an initial condition for T_1.
The first term of an arithmetic sequence is 5. The third term is 17.
The first term of an arithmetic sequence is 6. The fourth term is - 6.
Find the value of n if:
The nth term of the sequence 23, 14, 5, - 4 , \ldots is -238.
The nth term of the sequence \dfrac{2}{3}, \dfrac{11}{12}, \dfrac{7}{6}, \dfrac{17}{12}, \ldots is \dfrac{49}{6}.
In an arithmetic progression where a is the first term, and d is the common difference, we have T_2 = 9 and T_5 = 27.
Find d, the common difference.
Find a, the first term in the sequence.
State the general rule for T_n, the nth term in the sequence.
Hence, calculate T_{30}.
Solve for the value of x such that x + 4, 6 x + 5, and 9 x - 8 form successive terms in an arithmetic progression.
For each of the following graphs of sequences, state the recursive rule for T_n in terms of T_{n-1} as well as the initial term T_1:
For the following sequences given by the recursive rule:
State the explicit rule for T_n in terms of n.
Complete a table of values of the form:
| n | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| T_n |
Plot the points from the table of values on a graph.
Determine whether each point on the graph in part (c) would form a straight line.
T_{n + 1} = T_n + 3, T_1 = 5
T_{n + 1} = T_n + 4, T_1 = - 46
T_{n + 1} = T_n + 2.5, T_1 = 5
T_{n + 1} = T_n - 4, T_1 = 50
For the following graphs of arithmetic sequences:
Complete the table of values.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n |
Find the value of d.
Write the general rule for the nth term of the sequence, T_n.
Find the 12th term of the sequence.
For the following arithmetic sequences represented by a table of values:
Find d, the common difference.
Write the general rule for the nth term of the sequence, T_n.
Find T_{21}.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 5 | 11 | 17 | 23 |
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 6 | 2 | -2 | -6 |
For the sequence given by the recursive rule T_{n + 1} = T_n - 4, T_1 = 2:
Plot the first six points of the sequence on a graph.
State the explicit rule for T_n in terms of n.
State the first position n where the sequence becomes less than or equal to - 400.
For the sequence given by the recursive rule T_{n + 1} = T_n + 4, T_1 = - 1:
Plot the first six points of the sequence on a graph.
State the explicit rule for T_n in terms of n.
State the first position n where the sequence becomes greater than or equal to 500.