#### Linear number patterns,arithmetical sequences.

Do you still remember: The first term = T1 = a ; the common difference = d = Tn - Tn - 1 and
the general term = Tn = a + (n - 1)d ?
Now do the exercises below :
1.
Consider the following pattern / arithmetical sequence: 8; 13; 18; 23; . . .
1.1
Write down the next two terms and show how you calculated them.
1.2
Determine the formula / rule for the sequence [Determine T n ].
1.3
Calculate the value of T 18
1.4
Which term has a value of 108?
1.5
Determine n if Tn > 92
2.
Consider the following pattern / arithmetical sequence: 21; 27; 33; 39; . . .
2.1
Write down the next two terms and show how you calculated them.
2.2
Determine the formula / rule for the general term of the sequence.
2.3
Calculate the value of T 21
2.4
Which term has a value of 81?
2.5
Determine n if Tn > 200
3.
Consider the following pattern / arithmetical sequence: 62; 57; 52; 47; . . .
3.1
Write down the next two terms and show how you calculated them.
3.2
Determine the formula / rule for the general term of the sequence.
3.3
Evaluate T 8
3.4
Which term has a value of - 38?
3.5
Determine n so that Tn is the last positive term.
3.6
Determine n if Tn is the first negative term.
4.
Consider the following pattern / arithmetical sequence: 36; 30; 24; 18; . . .
4.1
Write down the next two terms and show how you calculated them.
4.2
Determine the formula / rule for the general term of the sequence.
4.3
Calculate the value of T 15
4.4
Which term has a value of - 24?
4.5
Determine n if Tn = 0
4.6
Determine n if Tn is the first negative term.
5.
Consider the following pattern / arithmetical sequence: - 68; - 61; - 54; - 47; . . .
5.1
Write down the next two terms and show how you calculated them.
5.2
Determine the formula / rule for the general term of the sequence.
5.3
Calculate the value of T 31
5.4
Which term has a value of - 19?
5.5
Determine n so that Tn is the first positive term.
6.
Consider the following pattern / arithmetical sequence: - 8; - 12; - 16; - 20; . . .
6.1
Write down the next two terms and show how you calculated them.
6.2
Determine the formula / rule for the general term of the sequence.
6.3
Calculate the value of T 15
6.4
Which term has a value of - 40?
6.5
Determine n if Tn is the last term smaller than - 100.
6.6
Determine T23 - T21
7.
Given that for an arithmetic sequence Tn = 7n - 3.
7.1
Write down the first two terms and show how you calculated them.
7.2
Determine T22 - T18.
8.
For an arithmetic sequence T21 = 89 and T33 = 137
8.1
Write down the first two terms and show how you calculated them.
8.2
Determine Tn .
8.3
Determine T26 .
9.
In an arithmetic sequence T11 = - 11 and T25 = - 53
9.1
Determine T17 .
9.2
Determine n so that Tn is the last positive term.
10.
In an arithmetic sequence T21 = 73 and T43 = 227
10.1
Determine T18 .
10.2
Determine n so that Tn is the last positive term.
11.
A linear sequence has T1 = 13 and T2 = 9
11.1
Find T12 .
11.2
Calculate the value of n if the nth term of the sequence is - 15.
12.
The first three terms of an arithmetic sequence are 3x - 1; 5x; 8x - 2
12.1
Determine the value of x and thus the first three terms of the sequence.
12.2
Determine the value of T9
13.
The first three terms of an arithmetic sequence are x + 3; 3x - 13; x - 9
13.1
Determine the value of x and thus the first three terms of the sequence.
13.2
Evaluate T11
14.
The first three terms of an arithmetic sequence are 18; x; 28
14.1
Determine the value of x and thus the formula of the general term.
14.2
Evaluate T8
14.3
Calculate the smallest value of n if Tn > 61