Consider the sequence defined by a_1 = 6 and a_n = a_{n - 1} + 5 for n \geq 2. Find:
The 21st term
The 22nd term
The 23rd term
The 24th term
The 25th term
Consider the first three terms of the following sequence: 9, 15, 21, \ldots
Find d, the common difference.
State the general rule for finding T_n.
Determine T_9.
Find the 90th term in the sequence.
Consider the sequence defined by a_1 = - 17, a_n = a_{n - 1} - 8 for n \geq 2.
Write a general rule for a_n, in terms of n.
Find the 90th term in the sequence.
Consider the sequence: 8.5, 3, - 2.5 , - 8 , \ldots
Write a general rule for a_n, in terms of n.
Find the 90th term in the sequence.
Consider the first three terms of the arithmetic sequence: 5, \dfrac{23}{4}, \dfrac{13}{2}, \ldots
Find d, the common difference.
State the expression for finding T_n.
Determine T_{14}.
In an arithmetic progression, T_{11} = 27 and T_{13} = 31.
Find the value of d.
Hence, find the value of a.
Find T_{10}.
In an arithmetic progression, T_5 = \dfrac{51}{5} and T_{15} = \dfrac{91}{5}.
Find the value of d.
Hence, find the value of a.
Find T_{27}.
In an arithmetic progression, the 6th term is -11 and the 8th term is -17.
Find the value of d.
Hence, find the value of a.
Hence, find the 14th term.
In an arithmetic progression, the first term is 32.
Write a simplfied 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 d.
For each of the following sequences, find the value of n given the nth term:
0.9, 1.5, 2.1, \ldots (nth term: 22.5)
2, 7, 12, \ldots (nth term: 132)
2, - 3 , - 8 , \ldots (nth term: - 578)
5, \dfrac{17}{4}, \dfrac{7}{2}, \ldots (nth term: - 37)
Find the value of x such that the following three terms form successive terms in an arithmetic progression:
The first three terms of an arithmetic progression are given by: 46, 41, 36, \ldots
Find the range of values of n for which the terms in the progression are positive.
Find the last positive term in the progression.
In an arithmetic progression, T_n = - 530. Solve for n given T_1 = 28 and d = - 18.
In an arithmetic progression, T_5 = 15 and T_{20} = 45.
Find the value of d.
Hence, find the value of a.
Find T_{10}.
Find the sum of the first 11 terms.
In an arithmetic progression, T_4 = 5.2 and T_{14} = 9.2.
Find the value of d.
Hence, find the value of a.
Find T_{26}.
Find the sum of the first 25 terms.
The first term of an arithmetic sequence is 3. The fifth term is 19.
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.
Find the 100th term in the sequence.
Consider the sequence: 7, 17, 27, 37, \ldots
Write a recursive rule for a_n in terms of a_{n - 1} and an initial condition for a_1.
Find the 100th term in the sequence.
For the sequences defined below:
Write a recursive rule for T_n in terms of T_{n - 1} and an initial condition for T_1.
Find the 100th term in the sequence.
Each term is obtained by decreasing the previous term by 5. The first term is 2.
Each term is obtained by increasing the previous term by 15. The first term is 20.
The nth term of a sequence starting from n = 1 is defined by T_n = - 6 - 3 \left(n - 1\right).
Write down the first four terms of the sequence.
Find d, the common difference.
Write a recursive rule for the sequence, and an initial condition for T_1.
For each of the following:
Determine the next four terms of the sequence, from T_2 to T_5.
Plot the first five terms on a graph.
Is the sequence generated from this definition arithmetic or geometric?
Consider the sequence plot drawn below:
State the first five terms of the sequence.
Is the sequence depicted by this graph arithmetic or geometric?
Write a recursive rule for t_n in terms of t_{n - 1} and an initial condition for t_1.
Consider the sequence: 4, 6, 8, 10, 12, \ldots
Plot the sequence on a graph.
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_1.
For the arithmetic progressions whose nth term is given by the folllowing equations:
Create a table of value for T_n using n = 1,2,3,4 and 10.
Find the difference between consecutive terms.
Plot the points in the table on the graph.
If the points on the graph were joined, would they form a straight or a curve?
Consider the following 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.
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.
In an arithmetic progression, T_5 = 26 and T_{10} = 51.
Find d, the common difference.
Find a, the first term.
State the general rule for T_n.
Hence, find T_{25}.
Find the sum of the first 25 terms.
The given table of values represents terms in an arithmetic sequence:
Find d, the common difference.
State the general rule for T_n.
Find the 17th term of the sequence.
Find the sum of the terms from T_{15} to T_{25} inclusive.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 8 | 13 | 18 | 23 |
The given table of values represents terms in an arithmetic sequence:
Find d, the common difference.
State the general rule for T_n.
Find the 13th term of the sequence.
Find the sum of the terms from T_{12} to T_{24} inclusive.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 6 | 1 | -4 | -9 |
The given table of values represents terms in an arithmetic sequence:
Find d, the common difference.
State the general rule for T_n.
Find the 13th term of the sequence.
Find the sum of the terms from T_{10} to T_{20} inclusive.
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| T_n | 6 | \dfrac{33}{4} | \dfrac{21}{2} | \dfrac{51}{4} |
The given table of values represents terms in an arithmetic sequence:
Find d, the common difference.
State the general rule for T_n.
Find the 20th term of the sequence.
Find the sum of the terms from T_8 to T_{30} inclusive.
| n | 1 | 3 | 5 | 7 |
|---|---|---|---|---|
| T_n | -1 | -21 | -41 | -61 |
The given table of values represents terms in an arithmetic sequence:
Find d, the common difference.
State the general rule for T_n.
Find the 20th term of the sequence.
Find the sum of the terms from T_{15} to T_{30} inclusive.
| n | 1 | 4 | 10 |
|---|---|---|---|
| T_n | 7 | -17 | -65 |