Linear number patterns or arithmetic sequences.

1.
Given the linear number patterns below. Calculate the next two terms of the
pattern and the formula for the general term, Tn
1.1
8;   13;   18;   . . .
1.2
38;   53;   68;   . . .
1.3
−23;   −15;   −7;   . . .
1.4
54;   41;   28;   . . .
2.
Study the following number pattern    :  7;   16;   25;   . . .
2.1
What kind of number pattern is this? Give a reason.
2.2
Calculate the value of
2.2.1
T11
2.2.2
n if Tn   =   124
3.
Study the following number pattern    :  28;   35;   42;   . . .
3.1
What kind of number pattern is this? Give a reason.
3.2
Calculate the value of
3.2.1
T18
3.2.2
n if Tn   =   203
4.
Given the following arithmetic sequence    :  18;   27;   36;   . . .
4.1
Calculate the formula for the general term, Tn .
4.2
Calculate the value of the 23rd term.
4.3
Calculate the number of the term that has a value of 288.
4.4
Which term is the last term that is smaller than 165?
4.5
Which term is the first term that is greater than 380?
5.
Given the following linear number pattern    :  53;   48;   43;   . . .
5.1
Calculate the value of T7 .
5.2
Calculate the value of n if Tn = −27 .
5.3
Which term is the last term that has a positive value?
5.4
Which term is the first negative term?
6.
Study the following linear number pattern    :  63;   55;   47;   . . .
6.1
Determine the formula for the general term, Tn.
6.2
Calculate the value of T7.
6.3
Calculate the number of the term which has a value of −25.
6.4
Which term is the last positive term?
7.
Study the following linear number pattern    :  −35;   −28;   −21;   . . .
7.1
Determine the formula for the general term, Tn.
7.2
Calculate the value of T18.
7.3
Calculate the number of the term which has a value of 35.
7.4
Which term is the first term greater than 110?
7.5
Which term is the last term smaller than 180?
8.
Study the following linear number pattern    :   87;   78;   69;   . . .
8.1
Determine the value of T13.
8.2
Which term has a value of 15?
8.3
Which term is the last term smaller than −60?
8.4
Which term is the first term greater than −94?
8.5
Which term is the first negative term?
9.
In a linear number pattern T10 =   44 and T19 =   80. Calculate the first three
terms of the pattern.
10.
T9 =   32 and T14 =   47 are two terms in the same linear number pattern.
Calculate the pattern [ Calculate the first three terms of the pattern].
11.
T5 =   5 and T12 =   −9   are two terms in the same linear number pattern.
Calculate the pattern [ Calculate the first three terms of the pattern].
12.
T6 =   −26 and T15 =   −53   are two terms in the same linear number pattern.
Calculate the first three terms of the pattern.
13.
T6 =   27 and T11 =   47 are two terms in the same linear number pattern.
13.1
Calculate the value of T15.
13.2
Calculate the value of n if Tn = 87
14.
In a linear number pattern T9 is 12 greater than T5 and T24 =   74.   Determine
the pattern.
15.
In an arithmetic sequence T21 is 30 greater than T6 and T13 =   33.
15.1
Determine the value of T10.
15.2
Which term has a value of 67?
16.
x − 2;   x + 2;  and 2x − 1  are the first three terms of a linear number pattern.
16.1
Calculate the value of x.
16.2
Determine the value of the ninth term.
17.
7x − 4;   5x + 5 and   4x + 6   are the first three terms of an arithmetic sequence.
17.1
Calculate the pattern.
17.2
Determine the value of the sixth term.
17.3
Determine the value of n such that Tn < 2 .
18.
2x − 2;   3x and   5x − 3   are the first three terms of an arithmetic sequence.
18.1
Calculate the pattern.
18.2
Determine the value of T8.
18.3
Which is the first term that has a value greater than 100?