Write down the next two terms for each arithmetic sequence:
4,8,12,16,\ldots
2,3.5,5,6.5,\ldots
6,2,- 2,- 6,\ldots
\dfrac{3}{4},\dfrac{2}{4},\dfrac{1}{4},\dfrac{0}{4},\ldots
- 8, - \dfrac{23}{3}, - \dfrac{22}{3}, - 7
Write the first four terms in each of the following arithmetic progressions:
The first term is - 10 and the common difference is 4
The first term is - 8 and the common difference is - 2
The first term is a and the common difference is d
Determine if the following sequences are arithmetic progressions:
3, 0, - 3 , - 6 , \ldots
1, 2, 3, 5, 8, 13, \ldots
3, 3^{3}, 3^{6}, 3^{9}, \ldots
4, - 4 , 4, - 4 , \ldots
5, 7, 5, 7,\ldots
State the common difference between consecutive terms of the following sequences:
3, 0, - 3 , - 6 , \ldots
330, 280, 230, 180, \ldots
- 6, - \dfrac{39}{7}, - \dfrac{36}{7}, - \dfrac{33}{7}, \ldots
Use the common difference to find missing terms in the following arithmetic progressions:
8,⬚,16,20,⬚
⬚,0,⬚,10,⬚
- 12,⬚,⬚,⬚,⬚,⬚,24
Find the first 3 terms of the sequences using the following recursive definitions:
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 each of the following, write a recursive rule for T_{n + 1} in terms of T_n and an initial condition for T_1:
Each term is obtained by increasing the previous term by 35. The first term is 60.
Each term is obtained by the previous term minus 4. The first term is 2.
The nth term of a sequence starting from n = 1 is defined by T_n = 5 n + 8.
Find the first four terms.
Find d, the common difference.
Write a recursive rule for the sequence, and an initial condition for T_1.
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.
Consider the arithmetic sequence with terms T_3 = 14 and T_{12} = 59.
Find d, the common difference.
Find the term T_1.
Write a recursive rule for T_n in terms of T_{n - 1} and an initial condition for T_1.
The nth term of a sequence is defined by: T_n = 11 + \left(n - 1\right) \times 10
Write down the first four terms of the sequence.
Find the common difference between consecutive terms in the sequence.
Consider the first three terms of the arithmetic sequence: 10, 3, - 4 \ldots
Determine the common difference.
State the equation for finding T_n, the nth term in the sequence.
Determine the 9th term in the sequence.
Consider the first three terms of the arithmetic sequence: 17, 16.2, 15.4 \ldots
Determine d, the common difference.
State the equation for finding T_n, the nth term in the sequence.
Determine T_{13} .
For each of the following arithmetic progressions:
Find a, the first term in the progression.
Find d, the common difference.
Find the indicated term.
T_n = 4 + 5 \left(n - 1\right),\ T_9
T_n = 2 - 6 \left(n - 1\right), \ T_8
T_n = - 2 + 6 \left(n - 1\right), \ T_7
T_n = - 4 - 5 \left(n - 1\right), \ T_5
T_n = 15 + 5 \left(n - 1\right), \ T_9
T_n = - 8 n + 28, \ T_5
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}.
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}.
For each of the following sequences:
State the recursive rule for T_n in terms of T_{n - 1}, and the initial term T_1.
State the explicit rule for T_n in terms of n.
Find the indicated term.
12, 15, 18, 21, \ldots (16th term)
22, 17, 12, 7, \ldots (21st term)
- 20 , - 16 , - 12 , - 8 , \ldots (26th term)
5, 6.5, 8, 9.5, \ldots (11th term)
The values in the table show terms in an arithmetic sequence for values of n:
Complete the table.
| n | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| T_n | -6 | -26 |
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 each of the following sequences given by a recursive rule:
State the explicit rule for T_n in terms of n.
Create a table of values for T_n using n = 1,2,3,4 and 10.
Plot the points from the table on a number plane.
State whether the points on the graph lie in a straight line.
T_{n + 1} = T_n + 3,\ T_1 = 5
T_{n + 1} = T_n - 4,\ T_1 = 50
T_{n + 1} = T_n + 4,\ T_1 = - 46
T_{n + 1} = T_n + 2.5,\ T_1 = 5
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 each of the following plotted points in the graphs:
Create a table of values for the given points.
Find d.
Write the general rule for T_n.
Find the indicated term in the sequence.
Find the 14th term.
Find the 18th term.
Find the 12th term.
Find the 11th term.
The plotted points represent terms in an arithmetic sequence:
Find d, the common difference.
Write a simplified expression for T_n.
If a line were drawn through the plotted points, find the gradient of the line.
The plotted points represent terms in an arithmetic sequence:
Find d.
Write a simplified expression for T_n.
The points are reflected across the horizontal axis to form three new points.
If these new points represent consecutive terms of an arithmetic sequence, write the general rule for A_n, the nth term in this new sequence.