Do you still remember: The first term = T_{1} = a ; the common difference = d = T_{n} - T_{n - 1} and

the general term = T_{n} = 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 T_{n} > 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 T_{n} > 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 T_{n} is the last positive term.

3.6

Determine n if T_{n} 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 T_{n} = 0

4.6

Determine n if T_{n} 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 T_{n} 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 T_{n} is the last term smaller than - 100.

6.6

Determine T_{23} - T_{21}

7.

Given that for an arithmetic sequence T_{n} = 7n - 3.

7.1

Write down the first two terms and show how you calculated them.

7.2

Determine T_{22} - T_{18}.

8.

For an arithmetic sequence T_{21} = 89 and T_{33} = 137

8.1

Write down the first two terms and show how you calculated them.

8.2

Determine T_{n} .

8.3

Determine T_{26} .

9.

In an arithmetic sequence T_{11} = - 11 and T_{25} = - 53

9.1

Determine T_{17} .

9.2

Determine n so that T_{n} is the last positive term.

10.

In an arithmetic sequence T_{21} = 73 and T_{43} = 227

10.1

Determine T_{18} .

10.2

Determine n so that T_{n} is the last positive term.

11.

A linear sequence has T_{1} = 13 and T_{2} = 9

11.1

Find T_{12} .

11.2

Calculate the value of n if the n^{th} 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 T_{9}

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 T_{11}

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 T_{8}

14.3

Calculate the smallest value of n if T_{n} > 61