1.

Given the linear number patterns below. Calculate the next two terms of the

pattern and the formula for the general term, T_{n}

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

T_{11}

2.2.2

n if T_{n} = 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

T_{18}

3.2.2

n if T_{n} = 203

4.

Given the following arithmetic sequence : 18; 27; 36; . . .

4.1

Calculate the formula for the general term, T_{n} .

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 T_{7} .

5.2

Calculate the value of n if T_{n} = −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, T_{n}.

6.2

Calculate the value of T_{7}.

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, T_{n}.

7.2

Calculate the value of T_{18}.

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 T_{13}.

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 T_{10} = 44 and T_{19} = 80. Calculate the first three

terms of the pattern.

10.

T_{9} = 32 and T_{14} = 47 are two terms in the same linear number pattern.

Calculate the pattern [ Calculate the first three terms of the pattern].

11.

T_{5} = 5 and T_{12} = −9 are two terms in the same linear number pattern.

Calculate the pattern [ Calculate the first three terms of the pattern].

12.

T_{6} = −26 and T_{15} = −53 are two terms in the same linear number pattern.

Calculate the first three terms of the pattern.

13.

T_{6} = 27 and T_{11} = 47 are two terms in the same linear number pattern.

13.1

Calculate the value of T_{15}.

13.2

Calculate the value of n if T_{n} = 87

14.

In a linear number pattern T_{9} is 12 greater than T_{5} and T_{24} = 74. Determine

the pattern.

15.

In an arithmetic sequence T_{21} is 30 greater than T_{6} and T_{13} = 33.

15.1

Determine the value of T_{10}.

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 T_{n} < 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 T_{8}.

18.3

Which is the first term that has a value greater than 100?