Write down the next two terms for each arithmetic sequence:
4, 8, 12, 16
2, 3.5, 5, 6.5
6, 2, - 2, - 6
- 8, - \dfrac{23}{3}, - \dfrac{22}{3}, - 7
State the common difference for each arithmetic sequence:
- 6, - \dfrac{39}{7}, - \dfrac{36}{7}, - \dfrac{33}{7}\ldots
330, 280, 230, 180\ldots
For each of the following arithmetic sequences:
Write the first four terms of the sequence.
Find the common difference.
T_n = 3 n + 8
T_n = 11 + \left(n - 1\right) \times 10
T_n = - 7 - 3 \left(n - 1\right)
Write the first four terms in each of the following arithmetic sequences:
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.
Find the missing terms in the following arithmetic sequences:
8, ⬚, 16, 20, ⬚
⬚, 0, ⬚, 10, ⬚
Determine whether each set of numbers is an arithmetic sequence:
1, \sqrt{5}, 5, 5 \sqrt{5}, \ldots
2, 2^{2}, 2^{4}, 2^{6}, \ldots
2, 0, - 2, - 4, \ldots
3, - 3, 3, - 3, \ldots
5, 7, 5, 7\ldots
State the common difference of the arithmetic sequence found in part (a).
For each general formula of an arithmetic sequence:
Determine a, the first term in the arithmetic sequence.
Determine d, the common difference.
Find the indicated term in the sequence.
T_n = 15 + 5 \left(n - 1\right);\enspace T_9
T_n = - 8 n + 28;\enspace T_5
Consider the first three terms of the following arithmetic sequences:
Find the common difference, d.
State T_n, the general rule for the nth term in the sequence.
Find the indicated term in the sequence.
5, 12, 19, \ldots ;\enspace T_{10}
17, 16.2, 15.4, \ldots ;\enspace T_{13}
10, 3, - 4, \ldots ; \enspace T_{9}
5, \dfrac{23}{4}, \dfrac{13}{2}, \ldots ;\enspace T_{14}
Consider the arithmetic sequence: 1.4, 2.3, 3.2, \ldots, 10.4
Determine d, the common difference.
Solve for n, the number of terms in the sequence.
Find the missing 5 terms in the arithmetic sequence which has - 12 as its first term and 24 as its last term:
- 12,\, ⬚,\, ⬚,\, ⬚,\, ⬚,\, ⬚,\, 24
Find the value of x such that x + 4, 6 x + 5, and 9 x - 8 form successive terms in an arithmetic sequence.
In an arithmetic sequence, T_5 = 21 and T_{19} = 77.
Find the value of d.
Find the value of a.
State the general rule for T_n.
Find T_{11}.
In an arithmetic sequence, T_7 = 44 and T_{14} = 86.
Find the value of d.
Find the value of a.
State the general rule for T_n.
Hence, find T_{25}.
In an arithmetic sequence, T_7 = 9 and T_{15} = 13.
Find the value of d.
Find the value of a.
State the general rule for T_n.
Find T_{26}.
In an arithmetic sequence with common difference d, the first term is 32.
Write a simplified expression for the 5th term.
Write a simplified expression for the 9th term.
Given that the 9th term is 4 times the 5th term, find the common difference d.
The first three terms of an arithmetic sequence are: 82, 75, 68, \ldots
Determine the number of positive terms in the sequence.
Find the last positive term in the sequence.
For each of the following sequences, find the value of n:
0.9, 1.5, 2.1, \ldots where T_n = 22.5
2, 7, 12, \ldots where T_n = 132
2, - 3 , - 8 , \ldots where T_n = - 578
5, \dfrac{17}{4}, \dfrac{7}{2}, \ldots where T_n = - 37
The nth term of an arithmetic sequence is T_n = - 530.
Find the value of n given that T_1 = 28 and d = - 18.
In an arithmetic sequence the 6th term is x and the 10th term is y.
Form an expression for d in terms of x and y.
Form an expression for a in terms of x and y.
Form an expression for the 16th term in terms of x and y.
Consider the recurrence relation: u_{n + 1} = u_n + 3 with initial term u_0.
Complete the table identifying the first 4 terms of the sequence in terms of u_0:
Express u_7 in terms of u_0.
Express u_n in terms of u_0.
| n | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| u_n |
The nth term of an arithmetic sequence is given by the equation T_n = 12 + 4 \left(n - 1\right).
Complete the table of values:
By how much are the consecutive terms in the sequence increasing?
| n | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| T_n |
Plot the points in the table on a coordinate plane.
If the points on the graph were joined, would they form a straight line or a curve?
The nth term of an arithmetic sequence is given by the equation T_n = 15 - 5 \left(n - 1\right).
Complete the table of values:
Find the difference between consecutive terms.
| n | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| T_n |
Plot the points in the table on a coordinate plane.
If the points on the graph were joined, would they form a straight line or a curve?
Each given table of values represents terms in arithmetic sequence. For each table:
Find d, the common difference.
Write a simplified expression for the general term, T_n.
Find the missing term in the table.
| n | 1 | 2 | 3 | 4 | 15 |
|---|---|---|---|---|---|
| T_n | 9 | 15 | 21 | 27 |
| n | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| T_n | 5 | -4 | -13 | -22 |
| n | 1 | 2 | 3 | 4 | 11 |
|---|---|---|---|---|---|
| T_n | 4 | \dfrac{17}{2} | 13 | \dfrac{35}{2} |
| n | 1 | 3 | 5 | 7 | 19 |
|---|---|---|---|---|---|
| T_n | -10 | -26 | -42 | -58 |
| n | 1 | 6 | 10 | 18 |
|---|---|---|---|---|
| T_n | -10 | -40 | -64 |
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 |
The plotted points represent terms in an arithmetic sequence.
Complete the table of values for the given points:
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n |
State the value of d, the common difference.
Write a simplified expression for the general term, T_n.
Find the 14th term of the sequence.
The plotted points represent terms in an arithmetic sequence.
Complete the table of values for the given points:
| n | 1 | 3 | 5 |
|---|---|---|---|
| T_n |
State the value of d, the common difference.
Write a simplified expression for the general term, T_n.
Find the 18th term of the sequence.
The plotted points represent terms in an arithmetic sequence.
State the value of d, the common difference.
Write a simplified expression for the general term, T_n.
Find the gradient of the line that passes through these points.
The plotted points represent terms in an arithmetic sequence.
State the value of d, the common difference.
Write a simplified expression for the general term, T_n.
The points are reflected about the horizontal axis to form three new points.
If these new points represent consecutive terms of an arithmetic sequence, write the equation for T_k, the kth term in this new sequence.
A diving vessel descends below the surface of the water at a constant rate so that the depth of the vessel after 1 minute, 2 minutes and 3 minutes is 50 metres, 100 metres and 150 metres respectively.
By how much is the depth increasing each minute?
Find the depth of the vessel after 4 minutes.
Write a recursive rule to define the vessel's depth as an arithmetic sequence in terms of d_{n+1} with first term d_1.
Find the depth of the vessel after 10 minutes.
For a fibre-optic cable service, Christa pays a one off amount of \$200 for installation costs and then a monthly fee of \$30.
Complete the table of values for the total cost \left(T\right) of Christa's service over n months.
By how much are consecutive terms in the sequence increasing?
| n | 1 | 2 | 3 | 4 | 18 |
|---|---|---|---|---|---|
| T |
Considering the table of values, plot the points corresponding to n = 1, 2, 3 and 4.
If the points on the graph were joined, would they form a straight or curved line?