8.02 Arithmetic sequences (Extended)
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 u_1 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
The nth term of a sequence is defined by: u_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 u_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 u_n, the nth term in the sequence.
Determine u_{13} .
For each of the following arithmetic progressions:
Find u_1, the first term in the progression.
Find d, the common difference.
Find the indicated term.
u_n = 4 + 5 \left(n - 1\right),\ u_9
u_n = 2 - 6 \left(n - 1\right), \ u_8
u_n = - 2 + 6 \left(n - 1\right), \ u_7
u_n = - 4 - 5 \left(n - 1\right), \ u_5
u_n = 15 + 5 \left(n - 1\right), \ u_9
u_n = - 8 n + 28, \ u_5
In an arithmetic progression where u_1 is the first term, and d is the common difference, we have u_2 = 9 and u_5 = 27.
Find d, the common difference.
Find u_1, the first term in the sequence.
State the general rule for u_n, the nth term in the sequence.
Hence, calculate u_{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 explicit rule for u_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)